Question

24x^2y+28xy-20y

Answer 1

do what?

Answer 2

Factor The GCF Of The Polynomial

Answer 3

What is the GCF of 24, 28 and 20?

Answer 4

4

Answer 5

Good, now what is the GCF of x^2y, xy and y?

Answer 6

This Is The Confusing Part

Answer 7

think of x and y as just numbers

Answer 8

let's say that x = 2 and y = 3


if that's the case, then


x^2y is 2^2*3

xy is 2*3

and y is just 3

So what do 2^2*3, 2*3 and 3 all have in common?

Answer 9

So Would It Be Three Thats The Biggest Factor There

Answer 10

yes, now generalize it...which basically means replace 3 with y (and 2 with x)


So y is the common factor


This is because y is present in all 3 expressions

Answer 11

Then combine the two GCFs to get 4y


This means that the GCF of 24x^2y , 28xy, and -20y is 4y

Answer 12

I Got 4x(6x+7x+5)........?????

Answer 13

It should be


4y(6x^2 + 7x - 5)


From there, can you factor 6x^2 + 7x - 5 further?

Answer 14

I Don't Think So

Answer 15

It turns out that you can. Here's why


Multiply the first coefficient and the last term: 6*(-5) = -30


Now find two numbers that multiply to -30 and add to 7. These two numbers are 10 and -3


Because such two numbers exist, this means that we can factor it further

Answer 16

So break up 7x into 10x-3x and factor by grouping


6x^2 + 7x - 5

6x^2 + 10x-3x - 5

(6x^2+10x)+(-3x-5)

2x(3x+5)-1(3x-5)

(2x-1)(3x-5)


So 6x^2 + 7x - 5 factors to (2x-1)(3x-5)


Therefore, 24x^2y+28xy-20y completely factors to 4y(2x-1)(3x-5)