Question

What must be subtracted from$8x^4+14x^3-2x^2+7x-8$ so that the resulting polynomial is exactly divisible by $g\left(x\right)=4x^2+3x-2$?

Answer 1

Find the resulting polynomial is exactly divisible by $g\left(x\right)=4x^2+3x-2$

Let subtract $y$ from $p\left(x\right)$$=8x^4+14x^3-2x^2+7x-8$

So,remainder will be zero

$$\begin{gathered} 14x-10-y=0 \\ \Rightarrow y=14x-10 \end{gathered}$$

Therefore, $p\left(x\right)$ should be deducted from $(14x-10)$ to make it exactly divisible by $g\left(x\right)$.