Answer:
(3x - 1) • (2x + 5)
Explanation:
Pull out like factors :
24x2 + 52x - 20 = 4 • (6x2 + 13x - 5)
Trying to factor by splitting the middle term
Factoring 6x2 + 13x - 5
The first term is, 6x2 its coefficient is 6 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 6 • -5 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is 13 .
-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7
-6 + 5 = -1
-5 + 6 = 1
-3 + 10 = 7
-2 + 15 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 15
6x2 - 2x + 15x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-1)
Add up the last 2 terms, pulling out common factors :
5 • (3x-1)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (3x-1)