Question B.4.4: Factoring ax² + bx + c with a ≠ 1 Factor each trinomial usin...
Factoring ax² + bx + c with a ≠ 1
Factor each trinomial using the ac-method.
a. 2x² + 5x + 2 b. 6x² – x – 12
a. Since ac = 2 ⋅ 2 = 4 and b = 5, we need two numbers that have a product of 4 and a sum of 5. The numbers are 4 and 1.
2 x^{2}+5 x+2=2 x^{2}+4 x+x+2 Replace 5x by 4x + x.
= (x + 2)2x + (x + 2)1 Factor by grouping.
= (x + 2)(2x + 1) Check using FOIL
b. Since ac = 6(-12) = -72 and b = -1, we need two numbers that have a product of -72 and a sum of -1. The numbers are 8 and -9.
6 x^{2}-x-12=6 x^{2}-9 x+8 x-12 Replace -x by -9x + 8x.
= (2x – 3)3x + (2x – 3)4 Factor by grouping.
= (2x – 3)(3x + 4) Check using FOIL.
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