Question

If the given polynomial $f\left(x\right)=x^4+a{x}^3-5x^2+7x-6,$ is divided by $x-3$ and leaves remainder as $-3$ then the value of $a$ is

• A. -2.0
• B. -02
• C. -2.00
• D. -2

Answer 1

Answer: (A), (B), (C), (D)

Given: $f\left(x\right)=x^4+a{x}^3-5x^2+7x-6.$

Remainder Theorem states that if a polynomial $p\left(x\right)$ is divided by $x-a$, then the remainder obtained is $p\left(a\right)$

On dividing $f\left(x\right)$ by $x-3$, the remainder obtained will be:
$f\left(3\right)=(3{)}^4+a(3{)}^3-5(3{)}^2+7(3)-6=-3$
$\Rightarrow f\left(3\right)=81+27a-45+21-6=-3$
$\Rightarrow 27a=-54$
$\Rightarrow a=-2$