/sci/ - Science & Math

[Anonymous No.5683967]

Hello /sci/

I have a basic algebra/arithmetic question.

I'm learning algebra from a book, no prof, and I'm at the step where I'm learning to factor polynomials, and I don't think I understand the logic behind one of the steps. I'm hoping someone could explain it to me.

So basically, I'm factoring:

15x^2+42x-9
3(5x^2+14x-3) --->GCF of 3
3(5x^2+15x-x-3) --->a x c = 15, 15-1 = b
3(5x^2+15x-x-3)
3(5x(x+3) -1(x+3)) ---> Up until here I understand. The final answer is:
3(5x-1)(x+3) ---> The part I don't understand is why the we're able to cancel one of the (x+3)s out. Can someone explain this to me?

Would be greatly appreciated.

Thanks /sci/

[Anonymous No.5683971]

You're not cancelling either one out.

What you're doing is combining them because:

5x * (x+3) - 1 * (x+3) = (5x-1)(x+3)

Since you're multiplying both by x+3 you can just combine them.

Think of it this way.

If it were just 5(x+3)-1(x+3) would that be the same as 4(x+3)?

Distribute it and find out.

[Anonymous No.5683981]

>>5683971
Hey, thanks so much man. Much clearer.

[Anonymous No.5683984]

>>5683981
No problem. I suck at math but I knew that one so I thought I'd help.

[Anonymous No.5683997]

>>5683981
Yeah, sometimes I also forget to see (x+3) as a whole "number", it's like forgetting that I am not only writing words here because I am also writing sentences.