CAIE IGCSE Additional Math 3 Factors of Polynomials Topic Practice

$\mathrm{p}^{\prime}(x)=9 x^{2}-14 x+a$ soi
$$\begin{aligned} \mathrm{p}^{\prime}(-1)=9+14+a=21 a=-2 \end{aligned}$$
p(2)=24-28+2 a+b=0 soi
Each term must be simplified, allow using their a

b=8

$[x-2]\left(3 x^{2}-x-4\right)$ soi

M1 for quadratic factor with two terms correct
A1 must be from correct a and b

(x-2)(x+1)(3 x-4)

A1

A1 must be from correct a and b

8 a-12-6+b=0 oe
and -a-3+3+b=0 oe
and a=2, b=2
B1 for 8 a-12-6+b=0 oe

B1 for -a-3+3+b=0 oe

and $x=2, \frac{1}{2},-1$

OR
$$\begin{aligned} {\left[2 x^{3}-3 x^{2}-3 x+2=\right] } & (x+1),\left(2 x^{2}-5 x+2\right) & \text { or }(x-2),\left(2 x^{2}+x-1\right) \end{aligned}$$

and correct factorisation or method of solution of the quadratic
$$\text { and } x=2, \frac{1}{2},-1$$

OR
$$2-1+x=-\left(\frac{-3}{2}\right) \text { or } 2-1+x=\frac{3}{2}$$

or for $2 \times-1 \times x=\frac{-2}{2}$ or $2 \times-1 \times x=-1$ and $x=2, \frac{1}{2},-1$
B1 for
$$\left[2 x^{3}-3 x^{2}-3 x+2=\right]$$
(x-2) and (x+1) seen
or ( $x^{2}-x-2$ ) seen
or $(x+1),\left(2 x^{2}-5 x+2\right)$
or $(x-2),\left(2 x^{2}+x-1\right)$
B1 for $2-1+x=-\left(\frac{-3}{2}\right)$ or $\frac{3}{2}$
or for $2 \times-1 \times x=\frac{-2}{2}$ or -1