(x^2 - 4x - 12)/(x^2 - 2x - 24)
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Answers
Step-by-step explanation:
x2 - 4x - 12
Simplify ————————————
x2 - 2x - 24
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
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 -4 .
-12 + 1 = -11
-6 + 2 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
x2 - 6x + 2x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
2 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-6)
Which is the desired factorization
Factoring x2-2x-24
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -2 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5
-6 + 4 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 4
x2 - 6x + 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
4 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-6)
Which is the desired factorization
Cancel out (x-6) which appears on both sides of the fraction line.
Final result :
x + 2
—————
x + 4