x^2-5x-84=================
Answers
Factoring x2-5x-84
The first term is, x2 its coefficient is 1 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -84
Step-1 : Multiply the coefficient of the first term by the constant 1 • -84 = -84
Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is -5 .
-84 + 1 = -83
-42 + 2 = -40
-28 + 3 = -25
-21 + 4 = -17
-14 + 6 = -8
-12 + 7 = -5
That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 7
x2 - 12x + 7x - 84
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
7 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+7) • (x-12)
Which is the desired factorization