Question

I'm a bit flustered. Can someone help me please?

Polynomial Division and the Remainder Theorem

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.

Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function.

Answer 1

You are told to divide a polynomial by a monomial, right? A monomial would be something like x + 3, and your polynomial could be something like x^2 + 7x + 12. The remainder theorem tells you that if you use long division to divide the polynomial by the monomial, if you have a remainder, the monomial is NOT a factor of the polynomial. You put the polynomial under the division sign and the monomial outside the division sign and do the dividing, just like you would if you had 80 under the division sign and 10 outside. When you divide the 80 by the 10, it comes out evenly with no remainder. Same thing with this: if you can divide x^2 + 7x + 12 by x + 3 and there is no remainder, then x + 3 is a factor of the polynomial. What's up on top above the division sign is the other factor. So when you multiply the x + 3 by what's on top, you get back your polyomial. It's really a very perfect and cool thing.