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.

Remainder is 12.

The binomial is not a factor of the given polynomial.

Step-by-step explanation:

The Remainder Theorem states that when a polynomial is divided by a binomial , then the remainder is given as .

Also, if is 0, then is a factor of the given polynomial.

Here, and

So, the remainder on dividing by is .

Now, .

Therefore, the remainder is 12.

∵   is equal to 12 and not 0. So, the binomial is not a factor of the given polynomial.

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step-by-step explanation: