Question

What must be subtracted from $4x^4-2x^3-6x^2+x-5,$ so that the result is exactly divisible by $2x^2+x-1$

• A. $-5$
• B. $-3$
• C. $-6$
• D. $-8$

Answer 1

Answer: (C)

$-6$

We have

$2x^2+x-1=0$

$\Rightarrow$$2x^2+2x-x-1=0$

$\Rightarrow$$2x(x+1)-1(x+1)=0$

$\Rightarrow$$(2x-1)(x+1)=0$

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

Let $p$ is subtracted from

$4x^4-2x^3-6x^2+x-5$

$\Rightarrow 4x^4-2x^3-6x^2+x-5-p$

Therefore,

$\Rightarrow$$4(-1{)}^4-2(-1{)}^3-6(-1{)}^2+(-1)-5-p=0$

$\Rightarrow$$4+2-6-1-5-p=0$

$\Rightarrow$$-p-6=0$

$\Rightarrow$$p=-6$