# IBDP Past Year Exam Questions – Polynomials

Q1. [M99.P1]

When the function  $f\left(x\right)=6{x}^{4}+11{x}^{2}–22{x}^{2}+ax+6$ is divided by $\left(x+1\right)$ the remainder is $–20$ . Find the value of  $a$ .[4]

Q2. [N99.P1]

The polynomial leaves a remainder of  $–1$ when divided by $\left(x+1\right)$ , and a remainder of 27 when divided by $\left(x–2\right)$ . Find the values of the real numbers $a$  and $b$ .[4]

Q3.   [N01.P1]

The polynomial $f\left(x\right)={x}^{3}+3{x}^{2}+ax+b$ leaves the same remainder when divided by $\left(x–2\right)$ as when divided by $\left(x+1\right)$ . Find the value of a.[3]

Q4.   [N02.P1]

When the polynomial ${x}^{4}+ax+3$ is divided by $\left(x–1\right)$ , the remainder is 8. Find the value of $a$ . [6]

Q5.  [M03.P1]

The polynomial ${x}^{3}+a{x}^{2}–3x+b$ is divisible by $\left(x–2\right)$  and has a remainder 6 when divided by $\left(x+1\right)$ . Find the value of $a$ and of $b$ .[6]

Q6.   [M04.P1]

The polynomial ${x}^{2}–4x+3$ is a factor of  ${x}^{3}+\left(a–4\right){x}^{2}+\left(3–4a\right)x+3$ . Calculate the value of the constant $a$ .  [6]

Q7.  [N04.P1]

Consider $f\left(x\right)={x}^{3}–2{x}^{2}–5x+k$ . Find the value of k if $\left(x+2\right)$ is a factor of $f\left(x\right)$ . [6]

Q8.  [N05.P1]

When the polynomial $P\left(x\right)=4{x}^{3}+p{x}^{2}+qx+1$  is divided by $\left(x–1\right)$ the remainder is $–2$ . When $P\left(x\right)$ is divided by $\left(2x–1\right)$ the remainder is . Find the value of $p$  and of $q$ . [6]

Q9.  [M06.P1]

The polynomial  $P\left(x\right)=2{x}^{3}+a{x}^{2}–4x+b$  is divisible by $\left(x–1\right)$ and by $\left(x+3\right)$ . Find the value of $a$  and of $b$ .[6]

Q10.   [N07.P1]

Given that  $\left(x–2\right)$ and  $\left(x+2\right)$ are factors of  $f\left(x\right)={x}^{3}+p{x}^{2}+qx+4$ , find the value of $p$  and of $q$ . [6]

Q11.   [M08.P1]

The polynomial  $P\left(x\right)={x}^{3}+a{x}^{2}+bx+2$ is divisible by $\left(x+1\right)$  and by $\left(x–2\right)$ . Find the value of $a$  and of $b$ , where  .[6]