Answer:
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14
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5.2 Factoring 15x2 - 11x - 14
The first term is, 15x2 its coefficient is 15 .
The middle term is, -11x its coefficient is -11 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 15 • -14 = -210
Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is -11 .
-210 + 1 = -209
-105 + 2 = -103
-70 + 3 = -67
-42 + 5 = -37
-35 + 6 = -29
-30 + 7 = -23
-21 + 10 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 10
15x2 - 21x + 10x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x-7)
Add up the last 2 terms, pulling out common factors :
2 • (5x-7)
Step-5 : Add up the four terms of step 4 :
(3x+2) • (5x-7)
Which is the desired factorization
