Question

I need help understanding exactly what they did to factor this trinomial?

They asked us to factor 15y^4+26y^3+7y^2

And then they said the correct answer was y^2(3y+1)(5y+7)

How did they get that answer?

Answer 1

they use GCF

Answer 2

Yeah but how??? I'm genuinley confused and I have no idea how they came acrooss the answer. I have a bunch of steps I was supposed to follow but they don't lead to that answer. Can someone show me how to do it and explain what's being done?

Answer 3

they first factored the GCF y^2 out to go from

15y^4+26y^3+7y^2

to

y^2 ( 15y^2 + 26y + 7 )

make sense so far?

Answer 4

Yes...

Answer 5

So y^2 is the GCF? And why did 15y^4 turn into 15y^2??

Answer 6

because 15y^4 divided by y^2 is 15y^2

Answer 7

or think backwards

if you distribute y^2 ( 15y^2 + 26y + 7 ) , you'll get 15y^4+26y^3+7y^2 again

Answer 8

see how I'm getting this?

Answer 9

Okay yeah I get it..

Answer 10

now just focus on the expression 15y^2 + 26y + 7

and ignore the y^2 outside the parenthesis for now

Answer 11

how do you factor 15y^2 + 26y + 7

Answer 12

No idea. I'm only used to factoring trinomials when the first part has no coefficient /:

Answer 13

you don't have too many choices, since 7 only factors as \(7\times 1\)

Answer 14

multiply 15 and 7 to get 105

then list all the ways to multiply to 105: 1*105, 5*21, etc

which of these pairs adds to 26?

Answer 15

5 and 21

Answer 16

so 26y breaks up into 5y + 21y and we can factor by grouping

Answer 17

15y^2+26y+7


15y^2+5y+21y+7


(15y^2+5y)+(21y+7)


5y(3y+1)+(21y+7)


5y(3y+1)+7(3y+1)


(5y+7)(3y+1)

Answer 18

This means


15y^2+26y+7


factors to


(5y+7)(3y+1)

Answer 19

of course, the order of the terms doesn't matter and we can easily say


15y^2+26y+7 factors to (3y+1)(5y+7)

Answer 20

the last thing to do is to add back in the GCF y^2 we ignored before when we factored 15y^2+26y+7

so that's why the answer is y^2(3y+1)(5y+7)

Answer 21

Do I absolutely have to ignore the y^2? Because I didn't and I got (3y+1)(5y^3+7y^2) and when I multiply my answer I get the original expression?

Answer 22

you can keep it in, but you would have to factor 5y^3+7y^2 down further

Answer 23

Oh okay. Thanks for all of your help, I appreciate it :)

Answer 24

you're welcome