factorize : 13x2+37x-6
Answers
Answer:
The first term is, 13x2 its coefficient is 13 .
The middle term is, +37x its coefficient is 37 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 13 • -6 = -78
Step-2 : Find two factors of -78 whose sum equals the coefficient of the middle term, which is 37 .
-78 + 1 = -77
-39 + 2 = -37
-26 + 3 = -23
-13 + 6 = -7
-6 + 13 = 7
-3 + 26 = 23
-2 + 39 = 37 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 39
13x2 - 2x + 39x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (13x-2)
Add up the last 2 terms, pulling out common factors :
3 • (13x-2)
Step-5 : Add up the four terms of step 4 :
(x+3) • (13x-2)
Which is the desired factorization