Question

Is the term (x + 2) a factor of the polynomial shown below?
f(x)=x^4+5x^3+10x^2+20x+24
A. Yes, the remainder is 48.
B. Yes, the remainder is 0.
C. No, the remainder is 48.
D. No, the remainder is 0.

Answer 1

Do you know how to do synthetic division?

Answer 2

i have an idea, but im not too confident in it. is that what i need to do?

Answer 3

would i do (x^4+5x^3+10x^2+20x+24) divided by (x+2)?

Answer 4

Yes. Then you'll find out if it's a factor, or, if not, what the remainder is.
(You can throw out 2 of those choices right away because they aren't logical)

Answer 5

Right. I can walk you through this one if you want.

Answer 6

First write all the coefficients, and the opposite of the divisor.

Answer 7

okay doing that now :)

Answer 8

Take the first number and just bring it down unchanged

Answer 9

Now multiply it times your divisor and move that over to the next column.

Answer 10

Are you following so far?

Answer 11

yes, I completed it and got 1, 3, 4, 12, 0. so does that mean that it would be yes, the remainder is 0 or no, the remainder is 0?

Answer 12

Yes. If the remainder is 0, it's a factor.

That's what I meant by two of the options not being logical. It's not a factor if there is a remainder, and if it's a factor, there won't be a remainder.

Answer 13

oh okay, thank you!! :)