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what is the GCF of 8,22, and 6 ?
Oh wait i think i get it hold on... 8= 2^3 22=2*11 6=2*3
is that right so far??
notice how 2 is a factor in each, so we can factor out 2 8x^2+22x-6 = 2(4x^2+11x - 3)
how would we factor 4x^2+11x - 3 ?
Wouldn't you start simplifying the problem?
multiply the first coefficient (4) and the last term (-3) 4*(-3) = -12 what two factors of -12 add to 11 ?
put another way: what two numbers multiply to -12 and add to 11?
Wait i am confused... i thought you couldn't combine terms unless they were like terms.... and would 3 be one
I'm not combining like terms
I'm asking for the two numbers because it will help factor
oh. Okay so 11 is a prime number so its only factor is one.
-12 could be 6,2,3,4
here are all of the ways to multiply two whole numbers to get -12 -1*12 -2*6 -3*4 -4*3 -6*2 -12*1 which pair of factors will add up to 11?
The first one
yep -1*12 = -12 -1 + 12 = 11
so we can break up the 11x into -1x + 12x
4x^2+11x - 3 4x^2-1x + 12x - 3
then we'd factor 4x^2-1x + 12x - 3 by grouping
group up the terms in pairs 4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) do you see what step is next?
specifically you factor each group
how can you factor 4x^2-1x ?
I don't know?
we can factor out x, agreed? 4x^2 - 1x = x(4x - 1)
oh yeah since they are like terms
how would you factor 12x - 3 ?
Wouldn't you just do 12 -3 and then add the x
what factors do 12 and 3 have in common?
12x and -3 aren't like terms
oh duh 3
yeah so 12x - 3 = 3(4x - 1)
4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) x(4x - 1) + 3(4x - 1)
what factor shows up twice?
the 4x-1 shows up twice
we can factor that out x(4x - 1) + 3(4x - 1) will turn into (x+3)(4x - 1)
so hopefully you see how 8x^2+22x-6 factors to 2(x+3)(4x - 1)
I think so
go over the steps a few times to make sure you have a solid grasp of it. you can ask questions if you aren't sure about a step or two