Question

Determine the Greatest Common Factor and simplify the expression.
24x + 32x2 - 26x

A. 2x(12+16x -13)
B. 3x(8 + 9x - 13)
C. 8x(3x + 4x2 - 3x)
D. 4x(6 + 8x - 4)

Answer 1

@imqwerty

Answer 2

I can help if you'd like :p

Answer 3

Yeah, could you explain this?

Answer 4

Sure! So, first thing is that its asking for the GREATEST common factor of the expression 24x + 32x^2 - 26x. What common and biggest term can go into 24, 32, and 26?

Answer 5

Hmm ok. 4?

Answer 6

mmm not quite. 24/4 = 6 so that checks, 32/4 = 8 so that checks, but 26/4 = 6.5 and we're looking for whole numbers. Perhaps something a bit smaller than 4? ;p

Answer 7

2 goes into all things even.

Answer 8

24/2 = 12
32 / 2 = 16
26 / 2 = 13

Answer 9

Yes! 4 cant work but 2 fits into all of them. What else is common with that expression, numbers aside?

Answer 10

I'm not so sure what else is, or what you mean by that. You mean a variable that appears the most?

Answer 11

Yeah. Isn't there an x-variable in all of the expression?

Answer 12

Yes, so the GCF is 2 and X

Answer 13

yes sir. so, pull that out of the expression and what happens to the inside?

Answer 14

Not so sure...:\

Answer 15

Are you say line up the problem with 2 and X?

Answer 16

Basically we found the GCF which is 2x so we can yank it out of 24x + 32x^2 -26x so that it looks like 2x(___ + ____ - ____)

Answer 17

but whats in the underscores? :P

Answer 18

The numbers.

Answer 19

The other numbers that aren't 2x

Answer 20

But what about the numbers with X in them?

Answer 21

yeah. youre essentially diving 2x out of all three since you pulled it out

Answer 22

well, for the inside we have to divide by 2x so it becomes (24x)/(2x) + (32x^2)/(2x) - 26x/2x.

Answer 23

So from all of this, we find the greatest GCF out of all of them, and we take it out. We divide the GCF by the number stated above in the problem 26 / 2 = 13 etc. So the answer would be A?

Answer 24

Yeah. The reason you would want to divide is because by pulling that 2x out you're now multiplying it by the inside. if we left the inside alone and we multiplied the 2x through the unchanged inside the expression we would get wouldnt match the original one.

Answer 25

so 2x(24x + 32x^2 - 26x) would be equal to 48x^2 + 64x^3 - 52x^2 which is not equal to the original expression

2x(24x/2x + 32x^2/2x - 26x/2x) satisfies that we pulled the 2x out

Answer 26

Ohhh

Answer 27

yup

Answer 28

Just curious is this Algebra I or II?