Question

Find the GCF of the terms of the polynomial.

20x4y + 25x2

A.
100x4y

B.
5x2

C.
4x2

D.
5x4y

Can someone explain how to do this problem? I got D but I don't think its right.

Answer 1

5 is the GCF of 20 and 25, so you are on the right track.

Answer 2

But the problem is with the variable term x^4y

Answer 3

x^4 = x*x*x*x

and

x^2 = x*x


In the terms above, how many times does x show up?

Answer 4

2 times..? I'm not sure whether your talking about the one the 4 or the 2 or all together.

Answer 5

it'll help you !!

Answer 6

well in x^4, there are 4 copies of x and in x^2 there are 2 copies of x

Answer 7

in both, there are two copies of x. This is the most copies of x they both share together

Answer 8

that's why the GCF of x^4 and x^2 is x^2

Answer 9

as for the y variables, there is a y in the first term but not in the second

Answer 10

so y is NOT part of the GCF

Answer 11

ohh now I get it. At first I was confused with the Y and the X but now I understand it :) Thank you!

Answer 12

so what is the overall GCF?

Answer 13

5x2 ?

Answer 14

perfect

Answer 15

Thank you so much! :)

Answer 16

btw, you type 5x^2 to mean \(\Large 5x^2\), but I know what you meant to say

Answer 17

you're welcome