Question

What must be added to the polynomial $P\left(x\right)=x^4+2x^3-2x^2+x-1$. So that the resulting polynomial is exactly divisible by $x^2+2x-3$?

• A. $x-1$
• B. $x-2$
• C. $x+1$
• D. $x+2$

Answer 1

The correct option is B $x-2$

Factors of $x^2+2x-3$ are $(x+3)$ and $(x-1)$.

If we use Synthetic Division for $x^4+2x^3-2x^2+x-1$, it should be divided by both $x+3$ and $x-1$.

therefore the term -(-x+2) should be added to $x^4+2x^3-2x^2+x-1$

By adding the term $x-2$ into $x^4+2x^3-2x^2+x-1$, we get the polynomial $x^4+2x^3-2x^2+2x-3$ which is exactly divisible by $x^2+2x-3$.

Hence, the term $x-2$ should be added.