Question

Say true or false:

For polynomials $p\left(x\right)$ and any non-zero polynomial $g\left(x\right)$, there are polynomials $q\left(x\right)$ and $r\left(x\right)$ such that $p\left(x\right)=g\left(x\right)q\left(x\right)+r\left(x\right)$, where $r\left(x\right)=0$ or degree $r\left(x\right)<$ degree $g\left(x\right).$ This statement is correctly explains the remainder theorem.

• A. True
• B. False

Answer 1

The correct option is A True

The Remainder theorem states that

For polynomials $p\left(x\right)$ and any non-zero polynomial $g\left(x\right)$, there are polynomials $q\left(x\right)$ and $r\left(x\right)$ such that $p\left(x\right)=g\left(x\right)q\left(x\right)+r\left(x\right)$, where $r\left(x\right)=0$ or degree $r\left(x\right)<$ degree $g\left(x\right).$

So, the given statement is the statement of Remainder theorem.

Hence, the given statement correctly explains the remainder theorem.