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The form x2 - bx + c ?
This tutorial will help you factor quadratics that look something like this:
x2 -7x + 12
(No leading coefficient; negative middle coefficient; positive constant coefficient.)
Step 1: Write down all the different ways to factor the constant coefficient (12) into two negative numbers:
12 = ( -1)(-12 )
12 = ( -2)( -6 )
12 = ( -3)( -4 )
(Order doesn't matter. So (-3)(-4) is the same as (-4)(- 3).)
Step 2: Now, for each possible factorization, add together the two factors. You're looking for two that add up to the middle coefficient, which is -7.
-1 - 12 = -13
-2 - 6 = -8
-3 - 4 = - 7 < --------------------------- found it!
The factors which worked out were -3 and -4, so here's how
you factor the polynomial:
(x - 3)(x - 4)
Step 3: Check your answer by multiplying out using FOIL:
(x - 3)(x - 4) = x2 - 7x + 12.
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