Question

Use the Remainder Theorem to find the remainder for (x^3-x+6) divided by (x-2) and state whether or not the binomial is a factor of the polynomial.

Answer 1

Answer:

Remainder is 12.

The binomial $(x-2)$ is not a factor of the given polynomial.

Step-by-step explanation:

The Remainder Theorem states that when a polynomial $p(x)$ is divided by a binomial $(x-a)$, then the remainder is given as $p(a)$.

Also, if $p(a)$ is 0, then $(x-a)$ is a factor of the given polynomial.

Here, $p(x)=x^{3}-x+6$ and $a=2$

So, the remainder on dividing $p(x)=x^{3}-x+6$ by $(x-2)$ is $p(2)$.

Now, $p(2)=2^{3}-2+6=8-2+6=12$.

Therefore, the remainder is 12.

∵  $p(2)$ is equal to 12 and not 0. So, the binomial $(x-2)$ is not a factor of the given polynomial.