Answer:
a. 2(x +2)(x +3)
b. (2x +3)(3x -2)
Step-by-step explanation:
a. First the common factor of 2 can be removed:
2(x^2 +5x +6)
Now, we're looking for factors of 6 that sum to 5
6 = 1·6 = 2·3 . . . . . the latter pair has a sum of 5
These constants go into the binomial factors directly:
2(x +2)(x +3)
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b. There are no common factors among the coefficients. We need to find factors of ac = (6)(-6) = -36 that have a sum of b = 5.
-36 = -1·36 = -2·18 = -3·12 = -4·9 = -6·6
The factor pair (-4, 9) has a sum of +5, so that is the one we're looking for. We can rewrite the middle term using these numbers, then factor by grouping.
6x² -4x +9x -6
2x(3x -2) +3(3x -2) . . . . . . factor the first pair of terms and the last pair
(2x +3)(3x -2) . . . . . . . . . . factor out the common factor of 3x-2
