Answer:
x+3
Step-by-step explanation:
x2 - x - 12
Simplify ———————————
x - 4
Trying to factor by splitting the middle term
1.1 Factoring x2 - x - 12
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
x2 - 4x + 3x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
3 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-4)
Which is the desired factorization
Canceling Out :
1.2 Cancel out (x-4) which appears on both sides of the fraction line.
Final result :
x + 3
