Question

Factoring help?
i have absolutely no idea how to do this, there are multiple problems like this and they didnt explain it very well. how would i go about solving this?

Factor completely: xy + 4y − 2x − 8

(x − 4)(y + 2)

(x + 4)(y − 2)

(x − 4)(x − 2)

Prime

Answer 1

x(y-2) + 4(y-2) = (x+4)(y-2)

Answer 2

Factoring is a little tricky if you've never done it before. You're pulling a value out of terms (dividing it out) but then leaving it as a multiplier on the outside of brackets.

example: \[ab - 2a = a(b-2)\]
see how we pulled an a out of each term, and left it as a multiplier on the outside? :O that is factoring.

In your equation xy +y4 -2x -8, do you see any terms that share a variable that you can pull out of them? :D

Answer 3

hmm, the 4 - 2?

Answer 4

my apologies if im wrong, never done factoring before

Answer 5

so a good place to start, is with the variables. notice that the first and 3rd term both have an x in them.
so lets pull an x out of each. x(y-2) +4y - 8
understand what i did?

Answer 6

oh, yeah, i kinda understand how you got that - so whats next?

Answer 7

4y-8 , hmm they both seem to have a 4 in common. lets try pulling a 4 out of each term.
4(y-2)

Answer 8

hmm, so we look for things that are similar or have a GCF then put that to the left?

Answer 9

Yes it will almost always work out that way. There might be times when you don't want to pull out the GREATEST common term, you'll see why in a minute :U but it won't happen very often

so the next step is kinda tricky, we've simplified the problem to x(y-2) + 4(y-2) yes?

Answer 10

yes, after arranging them into that expression, what do we do now?

Answer 11

btw, appreciate you explaining all this to me.

Answer 12

So this is a little tricky. Notice that they both have a (y-2) term? so lets pull that out of each term :D
and we get..
(y-2)[x+4]

Answer 13

wow, factoring is weird. so we combine the two multipliers and the two things in the parentheses to get the answer then?

Answer 14

you are pulling OUT the parentheseed(is that a word..? XD) term from each .. and then looking at what is left over

x(y-2) + 4(y-2) = (y-2) (x*_____ + 4*_____ )

since we divided out the (y-2), the space is just a 1 left over there on each term :O hopefully i didn't make that too confusing..

Answer 15

ohh, alright :) well ty for helping, really appreciate it