Question

If (x + 2) is a factor of p(x) = $a{x}^3+b{x}^2+x-6$ and when p(x) is divided by (x – 2) the remainder is 4, then a + b =

• A. 2
• B. 3
• C. -3
• D. -2

Answer 1

Answer: (A)

2

(x + 2) is a factor of p(x), so we have p (-2) = 0
$\Rightarrow a(-2{)}^3+b(-2{)}^3+(-2)-6=0$
$\Rightarrow -8a+4b=8$
$\Rightarrow -2a+b=2.....\left(i\right)$

p(x) leaves remainder 4 when divided by (x - 2) $\Rightarrow$ p(2) = 4
$\Rightarrow a(2x^3+b(2{)}^2+\left(2\right)-6)=4$
$\Rightarrow 8a+4b-4=4$
$\Rightarrow 8a+4b=8$
$\Rightarrow 2a+b=2....\left(ii\right)$

(i) + (ii) $\Rightarrow 2b=4\Rightarrow b=2$
$\therefore 2a+2=a\Rightarrow a=0$
$\therefore a+b=0+2=2$