tootsi123
  • tootsi123
Which of the following is polynomial factor of 8x^2+22x-6? A (4x-3) B (4x+3) C (8x-2) D (8x+3) E (8x+6)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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tootsi123
  • tootsi123
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
what is the GCF of 8,22, and 6 ?
tootsi123
  • tootsi123
Oh wait i think i get it hold on... 8= 2^3 22=2*11 6=2*3

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tootsi123
  • tootsi123
is that right so far??
jim_thompson5910
  • jim_thompson5910
notice how 2 is a factor in each, so we can factor out 2 8x^2+22x-6 = 2(4x^2+11x - 3)
jim_thompson5910
  • jim_thompson5910
how would we factor 4x^2+11x - 3 ?
tootsi123
  • tootsi123
Wouldn't you start simplifying the problem?
jim_thompson5910
  • jim_thompson5910
multiply the first coefficient (4) and the last term (-3) 4*(-3) = -12 what two factors of -12 add to 11 ?
jim_thompson5910
  • jim_thompson5910
put another way: what two numbers multiply to -12 and add to 11?
tootsi123
  • tootsi123
Wait i am confused... i thought you couldn't combine terms unless they were like terms.... and would 3 be one
jim_thompson5910
  • jim_thompson5910
I'm not combining like terms
jim_thompson5910
  • jim_thompson5910
I'm asking for the two numbers because it will help factor
tootsi123
  • tootsi123
oh. Okay so 11 is a prime number so its only factor is one.
tootsi123
  • tootsi123
-12 could be 6,2,3,4
jim_thompson5910
  • jim_thompson5910
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?
tootsi123
  • tootsi123
The first one
jim_thompson5910
  • jim_thompson5910
yep -1*12 = -12 -1 + 12 = 11
jim_thompson5910
  • jim_thompson5910
so we can break up the 11x into -1x + 12x
tootsi123
  • tootsi123
Oh okay...
jim_thompson5910
  • jim_thompson5910
4x^2+11x - 3 4x^2-1x + 12x - 3
jim_thompson5910
  • jim_thompson5910
then we'd factor 4x^2-1x + 12x - 3 by grouping
jim_thompson5910
  • jim_thompson5910
group up the terms in pairs 4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) do you see what step is next?
tootsi123
  • tootsi123
Simplify them.
jim_thompson5910
  • jim_thompson5910
specifically you factor each group
jim_thompson5910
  • jim_thompson5910
how can you factor 4x^2-1x ?
tootsi123
  • tootsi123
I don't know?
jim_thompson5910
  • jim_thompson5910
we can factor out x, agreed? 4x^2 - 1x = x(4x - 1)
tootsi123
  • tootsi123
oh yeah since they are like terms
jim_thompson5910
  • jim_thompson5910
how would you factor 12x - 3 ?
tootsi123
  • tootsi123
Wouldn't you just do 12 -3 and then add the x
jim_thompson5910
  • jim_thompson5910
what factors do 12 and 3 have in common?
jim_thompson5910
  • jim_thompson5910
12x and -3 aren't like terms
tootsi123
  • tootsi123
oh duh 3
jim_thompson5910
  • jim_thompson5910
yeah so 12x - 3 = 3(4x - 1)
jim_thompson5910
  • jim_thompson5910
4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) x(4x - 1) + 3(4x - 1)
jim_thompson5910
  • jim_thompson5910
what factor shows up twice?
tootsi123
  • tootsi123
one
jim_thompson5910
  • jim_thompson5910
what else
tootsi123
  • tootsi123
4
jim_thompson5910
  • jim_thompson5910
the 4x-1 shows up twice
jim_thompson5910
  • jim_thompson5910
we can factor that out x(4x - 1) + 3(4x - 1) will turn into (x+3)(4x - 1)
jim_thompson5910
  • jim_thompson5910
so hopefully you see how 8x^2+22x-6 factors to 2(x+3)(4x - 1)
tootsi123
  • tootsi123
I think so
jim_thompson5910
  • jim_thompson5910
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
tootsi123
  • tootsi123
Okay

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