Chapter 4.3, Problem 1CFU

To determine

To explain: How the Remainder Theorem and the Factor Theorem are related.

Explanation of Solution

Given information: Remainder Theorem and the Factor Theorem

Calculation:

The remainder Theorem states that if a polynomial $P\left(x\right)$ is divided by $x-r,$ the remainder is $P\left(r\right)$ .

The Factor Theorem states that the binomial $x-r$ is a factor if and only if $P\left(r\right)=0$ .

So, the connection is practical.

If a division problem has a remainder of 0, then the divisor is a factor of the dividend.

Meaning that, if we find a value for which this remainder is zero, we can partially factorize the polynomial.