{"id":1050,"date":"2020-03-05T03:36:36","date_gmt":"2020-03-05T03:36:36","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1050"},"modified":"2020-03-05T12:33:53","modified_gmt":"2020-03-05T12:33:53","slug":"ibdp-past-year-exam-questions-polynomials","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/polynomials\/ibdp-past-year-exam-questions-polynomials\/","title":{"rendered":"IBDP Past Year Exam Questions &#8211; Polynomials"},"content":{"rendered":"<p><strong>Q1. [M99.P1]<\/strong><\/p>\r\n<p>When the function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mn>6<\/mn><msup><mi>x<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mn>11<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>22<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><\/math>\r\n is divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n the remainder is \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8211;<\/mo><mn>20<\/mn><\/math>\r\n . Find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n .[4]<\/p>\r\n<div id=\"link1-link-1050\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link1-content-1050\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1056\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1.jpg\" alt=\"\" width=\"1077\" height=\"295\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1.jpg 1077w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-300x82.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-1024x280.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-768x210.jpg 768w\" sizes=\"auto, (max-width: 1077px) 100vw, 1077px\" \/>\u00a0<\/div>\r\n<p><strong>Q2. [N99.P1] <\/strong><\/p>\r\n<p>The polynomial \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mo>&#160;<\/mo><msup><mfenced><mrow><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><\/mfenced><mn>3<\/mn><\/msup><\/math>\r\n leaves a remainder of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8211;<\/mo><mn>1<\/mn><\/math>\r\n when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n , and a remainder of 27 when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n . Find the values of the real numbers \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <em>\u00a0<\/em>and <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n .<\/em>[4]<\/p>\r\n<div id=\"link2-link-1050\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link2-content-1050\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1057\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2.jpg\" alt=\"\" width=\"1079\" height=\"342\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2.jpg 1079w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-300x95.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-1024x325.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-768x243.jpg 768w\" sizes=\"auto, (max-width: 1079px) 100vw, 1079px\" \/>\u00a0<\/div>\r\n<p><strong>Q3.\u00a0 \u00a0[N01.P1] <\/strong><\/p>\r\n<p>The polynomial \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/math>\r\n leaves the same remainder when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n as when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n . Find the value of <em>a<\/em>.[3]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/p>\r\n<div id=\"link3-link-1050\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link3-content-1050\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1058\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3.jpg\" alt=\"\" width=\"1178\" height=\"182\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3.jpg 1178w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-300x46.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-1024x158.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-768x119.jpg 768w\" sizes=\"auto, (max-width: 1178px) 100vw, 1178px\" \/><\/p>\r\n<p><\/div>\r\n<p><strong>Q4.\u00a0 \u00a0[N02.P1] <\/strong><\/p>\r\n<p>When the polynomial \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><\/math>\r\n is divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n , the remainder is 8. Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <em>. <\/em>[6]<\/p>\r\n<div id=\"link4-link-1050\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link4-content-1050\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1059\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4.jpg\" alt=\"\" width=\"1024\" height=\"154\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-300x45.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-768x116.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\u00a0<\/div>\r\n<p>\u00a0 <strong>Q5.<\/strong>\u00a0 <strong>[M03.P1]<\/strong><\/p>\r\n<p>The polynomial \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/math>\r\n is divisible by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n \u00a0and has a remainder 6 when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n . Find the value of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <\/em>and of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n <\/em>.[6]<\/p>\r\n<div id=\"link5-link-1050\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link5-content-1050\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1060\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5.jpg\" alt=\"\" width=\"964\" height=\"144\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5.jpg 964w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-300x45.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-768x115.jpg 768w\" sizes=\"auto, (max-width: 964px) 100vw, 964px\" \/><\/p>\r\n<p><\/div>\r\n<p><strong>Q6.\u00a0 \u00a0[M04.P1]<\/strong><\/p>\r\n<p>The polynomial \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><\/math>\r\n is a factor of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mfenced><mrow><mi>a<\/mi><mo>&#8211;<\/mo><mn>4<\/mn><\/mrow><\/mfenced><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfenced><mrow><mn>3<\/mn><mo>&#8211;<\/mo><mn>4<\/mn><mi>a<\/mi><\/mrow><\/mfenced><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><\/math>\r\n . Calculate the value of the constant <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <\/em>.\u00a0 [6]<\/p>\r\n<div id=\"link6-link-1050\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link6-content-1050\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1064\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-1.jpg\" alt=\"\" width=\"970\" height=\"694\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-1.jpg 970w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-1-300x215.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-1-768x549.jpg 768w\" sizes=\"auto, (max-width: 970px) 100vw, 970px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>Q7.\u00a0 <\/strong><strong>[N04.P1]<\/strong><\/p>\r\n<p>Consider \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>&#8211;<\/mo><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mi>k<\/mi><\/math>\r\n . Find the value of <em>k <\/em>if \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n is a factor of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><\/math>\r\n . [6]<\/p>\r\n<div id=\"link7-link-1050\" class=\"sh-link link7-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link7', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link7-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link7-content-1050\" class=\"sh-content link7-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>Q8.\u00a0 [N05.P1] <\/strong><\/p>\r\n<p>When the polynomial <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>p<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>q<\/mi><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/math>\r\n <\/em>\u00a0is divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n the remainder is \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8211;<\/mo><mn>2<\/mn><\/math>\r\n . When \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mfenced><mi>x<\/mi><\/mfenced><\/math>\r\n is divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mn>2<\/mn><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n the remainder is . Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n <em>\u00a0<\/em>and of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>q<\/mi><\/math>\r\n <\/em>. [6]<\/p>\r\n<div id=\"link8-link-1050\" class=\"sh-link link8-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link8', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link8-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link8-content-1050\" class=\"sh-content link8-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>Q9.\u00a0 [M06.P1] <\/strong><\/p>\r\n<p>The polynomial\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mn>2<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/math>\r\n \u00a0is divisible by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n and by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfenced><\/math>\r\n . Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <em>\u00a0<\/em>and of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n .<\/em>[6]<\/p>\r\n<div id=\"link9-link-1050\" class=\"sh-link link9-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link9', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link9-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link9-content-1050\" class=\"sh-content link9-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1065\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/9-1.jpg\" alt=\"\" width=\"1024\" height=\"195\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/9-1.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/9-1-300x57.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/9-1-768x146.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>Q10.\u00a0 \u00a0[N07.P1] <\/strong><\/p>\r\n<p>Given that\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n are factors of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>p<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>q<\/mi><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><\/math>\r\n , find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n <em>\u00a0<\/em>and of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>q<\/mi><\/math>\r\n <\/em>. [6]<\/p>\r\n<div id=\"link10-link-1050\" class=\"sh-link link10-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link10', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link10-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link10-content-1050\" class=\"sh-content link10-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1066\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/10.jpg\" alt=\"\" width=\"1119\" height=\"583\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/10.jpg 1119w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/10-300x156.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/10-1024x534.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/10-768x400.jpg 768w\" sizes=\"auto, (max-width: 1119px) 100vw, 1119px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>Q11.\u00a0 \u00a0[M08.P1] <\/strong><\/p>\r\n<p>The polynomial\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/math>\r\n is divisible by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n \u00a0and by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n . Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n <em>\u00a0<\/em>and of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n <\/em>, where\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>b<\/mi><mo>&#160;<\/mo><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8484;<\/mi><\/math>\r\n .[6]\u00a0 \u00a0 \u00a0 \u00a0<\/p>\r\n<div id=\"link11-link-1050\" class=\"sh-link link11-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link11', 1050, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link11-toggle-1050\">Solution<\/span><\/a><\/div><div id=\"link11-content-1050\" class=\"sh-content link11-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1067\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/11.jpg\" alt=\"\" width=\"942\" height=\"771\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/11.jpg 942w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/11-300x246.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/11-768x629.jpg 768w\" sizes=\"auto, (max-width: 942px) 100vw, 942px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>&nbsp;<\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"Q1. [M99.P1] When the function\u00a0 fx=6&#215;4+11&#215;2&#8211;22&#215;2+ax+6 is divided by x+1 the remainder is &#8211;20 . Find the value of\u00a0 a .[4] Q2. [N99.P1] The polynomial px=&#160;ax+b3 leaves a remainder of\u00a0 &#8211;1 when divided by x+1 , and a remainder of 27 when divided by x&#8211;2 . Find the values of the real numbers a \u00a0and [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1050","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-polynomials","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1050"}],"version-history":[{"count":7,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1050\/revisions"}],"predecessor-version":[{"id":1068,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1050\/revisions\/1068"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}