{"id":1814,"date":"2020-05-25T06:25:24","date_gmt":"2020-05-25T06:25:24","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&p=1814"},"modified":"2020-07-01T08:08:29","modified_gmt":"2020-07-01T08:08:29","slug":"practice-questions-polynomials","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/polynomials\/practice-questions-polynomials\/","title":{"rendered":"Practice Questions – Polynomials"},"content":{"rendered":"

1. The cubic polynomial\u00a0 \r\nf<\/mi>(<\/mo>x<\/mi>)<\/mo><\/math>\r\n is defined by\u00a0 \r\nf<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>x<\/mi>3<\/mn><\/msup>+<\/mo>a<\/mi>x<\/mi>2<\/mn><\/msup>+<\/mo>14<\/mn>x<\/mi>+<\/mo>a<\/mi>+<\/mo>1<\/mn><\/math>\r\n
\r\nwhere \r\na<\/mi><\/math>\r\n <\/em> is a constant. It is given that\u00a0 \r\nx<\/mi>+<\/mo>2<\/mn><\/mrow><\/mfenced><\/math>\r\n is a factor of \r\nf<\/mi>(<\/mo>x<\/mi>)<\/mo><\/math>\r\n .
\r\n(i) Use the factor theorem to find the value of a<\/em> and hence factorise\u00a0 \r\nf<\/mi>(<\/mo>x<\/mi>)<\/mo><\/math>\r\n completely.[5 marks]<\/p>\r\n

(ii) Hence, without using a calculator, solve the equation \r\nf<\/mi>(<\/mo>2<\/mn>x<\/mi>)<\/mo>=<\/mo>3<\/mn>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/math>\r\n . [4 marks]<\/p>\r\n