Question

GIVE A MEDAL FOR WHO ANSWERS
Which student factored the expression x3 - 7x - x2 + 7 correctly based on their answer below?

Jane: (x + 1)(x2 - 7)
Mariah: (x - 1)(x2 + 7)
Roger: (x + 1)(x2 + 7)
Nethan: (x - 1)(x2 - 7)

Answer 1

HELP PLEASe

Answer 2

Do you know how to use the distributive method to check the given answers?

Answer 3

This is a simple FOIL (First, Outer, Inner, Last) question. So we will start with Jane's answer and create a polynomial with her answer and compare it to the given polynomial.

Answer 4

Jane's answer is (x + 1)(x^2 - 7). Using FOIL, we take the first term from the first factor and the first term from the second factor. (x) * (x^2) gives us x^3

Answer 5

Now we take the outer terms +1 and -7. Multiply these two together and we get -7. Since the final term of the given polynomial is +7, we can at this point discard Jane's answer as incorrect.

Answer 6

Moving on to Mariah's answer, we have (x - 1)(x^2 +7). Looking at her outer factors, we see that once again the final term of Mariah's polynomial will be -7, so we can quickly discard Mariah's answer as incorrect.

Answer 7

Roger's answer of (x + 1)(x2 + 7) is beginning to have some promise, so let's start expanding his factors back into a polynomial. We already know that (x) * (x^2) = x^3 and that +1 * +7 = +7, so we have our first and last terms of the polynomial matching. now let's look at the inner terms. (x) * (+7) gives us 7x which does not match the polynomial, so we can stop here and discard Roger's answer.

Answer 8

By process of elimination, that leaves us with Nethan's answer as correct, but let's check his math just to be sure.

Answer 9

Nethan answered (x - 1)(x^2 - 7). (x) * (x^2) = x^3, which matches the given polynomial. Now we multiply the outer terms, (-1) * (-7) = +7. So far, the terms are matching up.

Answer 10

Keep going and multiply (-1) * (x^2). This gives us -x^2. Still matching up.

Answer 11

Now we multiply (x) * (-7) = -7x. Take all the terms and combine them from greatest to least and we get x^3 - x^2 - 7x + 7, which indeed matches the given polynomial

Answer 12

Hope this helps!

Answer 13

Was Nethan correct? I thought it was Mariah...