Answer: (-6x - 5) • (2x + 3)
Step-by-step explanation:
((0 - (22•3x2)) - 28x) - 15
Pull out like factors :
-12x2 - 28x - 15 = -1 • (12x2 + 28x + 15)
Trying to factor by splitting the middle term
3.2 Factoring 12x2 + 28x + 15
The first term is, 12x2 its coefficient is 12 .
The middle term is, +28x its coefficient is 28 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 12 • 15 = 180
Step-2 : Find two factors of 180 whose sum equals the coefficient of the middle term, which is 28 .
-180 + -1 = -181
-90 + -2 = -92
-60 + -3 = -63
-45 + -4 = -49
-36 + -5 = -41
-30 + -6 = -36
-20 + -9 = -29
-18 + -10 = -28
-15 + -12 = -27
-12 + -15 = -27
-10 + -18 = -28
-9 + -20 = -29
-6 + -30 = -36
-5 + -36 = -41
-4 + -45 = -49
-3 + -60 = -63
-2 + -90 = -92
-1 + -180 = -181
1 + 180 = 181
2 + 90 = 92
3 + 60 = 63
4 + 45 = 49
5 + 36 = 41
6 + 30 = 36
9 + 20 = 29
10 + 18 = 28 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 10 and 18
12x2 + 10x + 18x + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (6x+5)
Add up the last 2 terms, pulling out common factors :
3 • (6x+5)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (6x+5)
Which is the desired factorization
<u>Answer:</u> (-6x - 5) • (2x + 3)
