Question

What must be added to $f\left(x\right)=4x^3+8x^2-7x+3\text{so that resulting polynomial is divisible}byg\left(x\right)=x^2-x+2?$

• A.
  $-19x-11$
• B.
  $19x+11$
• C.
  $18x-11$
• D.
  $19x-11$

Answer 1

The correct option is D

$19x-11$
$f\left(x\right)=g\left(x\right)\times q\left(x\right)+r\left(x\right)\Rightarrow f\left(x\right)+(-r(x\left)\right)=g\left(x\right)\times q\left(x\right)+r\left(x\right)+(-r(x\left)\right)\therefore f\left(x\right)+(-r(x\left)\right)=g\left(x\right)\times q\left(x\right)+0$



$r\left(x\right)=-19x+11-r\left(x\right)=-(-19x+11)=19x-11\Rightarrow (19x-11)\text{should be added to f(x)}\text{to make it exactly divisible by g(x)}$
So, the correct option is d.