9x²-24x=65 solve by
factorization
Answers
Step-by-step explanation:
Factoring 9x2-24x-65
The first term is, 9x2 its coefficient is 9 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is -65
Step-1 : Multiply the coefficient of the first term by the constant 9 • -65 = -585
Step-2 : Find two factors of -585 whose sum equals the coefficient of the middle term, which is -24 .
-585 + 1 = -584
-195 + 3 = -192
-117 + 5 = -112
-65 + 9 = -56
-45 + 13 = -32
-39 + 15 = -24 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -39 and 15
9x2 - 39x + 15x - 65
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x-13)
Add up the last 2 terms, pulling out common factors :
5 • (3x-13)
Step-5 : Add up the four terms of step 4 :
(3x+5) • (3x-13)
Which is the desired factorization
I hope it helps you