Question

If the expression $a{x}^4+b{x}^3-x^2+2x+3$ has remainder $4x+3$ when divided by $x^2+x-2$, then the value of $b-a$ is

• A. 1
• B. 1.00
• C. 1.0

Answer 1

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

Let $f\left(x\right)=a{x}^4+b{x}^3-x^2+2x+3$
Now, $x^2+x-2=(x+2)(x-1)$
$f(-2)=a(-2{)}^4+b(-2{)}^3-(-2{)}^2+2(-2)+3=4(-2)+3$
$\Rightarrow 16a-8b=0$
$\Rightarrow 2a-b=0\dots \left(i\right)$
Also, $f\left(1\right)=a(1{)}^4+b(1{)}^3-(1{)}^2+2(1)+3=4(1)+3$
$\Rightarrow a+b=3\dots \left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right),$ $a=1,b=2$
$\therefore b-a=2-1=1$