Please help me factor the following:
6x²-7x-3
6x²-7x-3
Multiply the green 6 times the red -3.
That gives -18.
Think of two integers which have
1. Product = -18
2. Sum = the blue -7
Such a pair of integers are -9 and +2
because
1. Product = (-9)x(+2) = -18
2. Sum = (-9)+(+2) = -7
Replace the middle term -7x by -9x + 2x, using
the -9 and the +2 as coefficients of x.
6x² - 9x + 2x - 3
Factor the first two terms by taking out GCF 3x
6x² - 9x + 2x - 3
3x(2x - 3) + 2x - 3
Factor the last two terms by taking out GCF = +1
(When there is nothing bigger that can be factored out,
then factor out +1 if the next to last term is
positive, or -1 if it is negative.)
3x(2x - 3) + 2x - 3
3x(2x - 3) + 1(2x - 3)
Now notice that the red expression (2x - 3) appears
in both terms as shown by the colors below:
3x(2x - 3) + 1(2x - 3)
So factor out the red expression (2x - 3) and
place the black parts inside parentheses:
3x(2x - 3) + 1(2x - 3)
(2x - 3)(3x + 1)
That's it, and you can just make it all black:
(2x - 3)(3x + 1)
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That's the answer. You can check it by FOIL:
6x² + 2x - 9x - 3
and combining the middle two terms:
6x² - 7x - 3
which is what we started with, so
(2x - 3)(3x + 1) is the correct factorization.
Edwin
