Question

If $(x-2)(x+a)(x-b)$ is the factorised form of the polynomial $(x^3-2x^2-9x+18),$ then find the values of $a$ and $b.$

• A. $a=3b=-3$
• B. $a=-3b=3$
• C. $a=3b=3$
• D. $a=-3b=-3$

Answer 1

The correct option is C $a=3b=3$

$p\left(x\right)=(x^3-2x^2-9x+18)$
One factor = $(x-2)$

Using synthetic division,
$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 1& 2& -9& 18\\ 1& \downarrow & 2& 0& -18\\ & 1& 0& -9& |-0\end{array}$

$\therefore p\left(x\right)=(x-2)(x^2-9)\text{Now,}{x}^2-9=x^2-3^2=(x+3)(x-3)=(x+3)(x-3)\text{Hence,}{x}^3-2x^2+9x+18=(x-1)(x+3)(x-3)$

Comparing it with the factorised form,
$a=3b=3$