Question

On dividing $x^4-2x^2-9x-9$ by a polynomial g(x), the quotient is $(x^2-x-4)\text{and the remainder is (3-2x).}\text{Find g(x)}$

• A.
  $x^2+x-3$
• B.
  $x^2+x+3$
• C.
  $x^2-x+3$
• D.
  $-x^2+x+3$

Answer 1

The correct option is B

$x^2+x+3$
$f\left(x\right)=x^4+2x^2-9x-9q\left(x\right)=x^2-x-4r\left(x\right)=3-2xg\left(x\right)\times q\left(x\right)+r\left(x\right)=f\left(x\right)\Rightarrow g\left(x\right)\times q\left(x\right)=f\left(x\right)-r\left(x\right)\Rightarrow g\left(x\right)=\frac{f\left(x\right)-r\left(x\right)}{q\left(x\right)}f\left(x\right)-r\left(x\right)=(x^4-2x^2-9x-9)-(3-2x)\Rightarrow x^4-2x^2-7x-12\therefore \frac{f\left(x\right)-r\left(x\right)}{q\left(x\right)}=\frac{x^4-2x^2-7x-12}{x^2-x-4}$


$g\left(x\right)=x^2+x+3$
So, correct option is b.