Answer:
6
—————
n + 8
Explanation:
Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
((12•(n3))-(24•(n2))) (12n-42)
—————————————————————•———————————————————
(((4•(n2))-22n)+28) ((6•(n3))+(24•3n2))
STEP
2
:
Equation at the end of step
2
:
((12•(n3))-(24•(n2))) (12n-42)
—————————————————————•——————————————————
(((4•(n2))-22n)+28) ((2•3n3)+(24•3n2))
STEP
3
:
12n - 42
Simplify ——————————
6n3 + 48n2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
12n - 42 = 6 • (2n - 7)
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
6n3 + 48n2 = 6n2 • (n + 8)
Equation at the end of step
5
:
((12•(n3))-(24•(n2))) (2n-7)
—————————————————————•————————
(((4•(n2))-22n)+28) n2•(n+8)
STEP
6
:
Equation at the end of step
6
:
((12•(n3))-(24•(n2))) (2n-7)
—————————————————————•————————
((22n2-22n)+28) n2•(n+8)
STEP
7
:
Equation at the end of step
7
:
((12•(n3))-(23•3n2)) (2n-7)
————————————————————•————————
(4n2-22n+28) n2•(n+8)
STEP
8
:
Equation at the end of step
8
:
((22•3n3) - (23•3n2)) (2n - 7)
————————————————————— • ————————————
(4n2 - 22n + 28) n2 • (n + 8)
STEP
9
:
12n3 - 24n2
Simplify ——————————————
4n2 - 22n + 28
STEP
10
:
Pulling out like terms
10.1 Pull out like factors :
12n3 - 24n2 = 12n2 • (n - 2)
STEP
11
:
Pulling out like terms
11.1 Pull out like factors :
4n2 - 22n + 28 = 2 • (2n2 - 11n + 14)
Trying to factor by splitting the middle term
11.2 Factoring 2n2 - 11n + 14
The first term is, 2n2 its coefficient is 2 .
The middle term is, -11n its coefficient is -11 .
The last term, "the constant", is +14
Step-1 : Multiply the coefficient of the first term by the constant 2 • 14 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4
2n2 - 7n - 4n - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (2n-7)
Add up the last 2 terms, pulling out common factors :
2 • (2n-7)
Step-5 : Add up the four terms of step 4 :
(n-2) • (2n-7)
Which is the desired factorization
Canceling Out :
11.3 Cancel out (n-2) which appears on both sides of the fraction line.
Equation at the end of step
11
:
6n2 (2n - 7)
—————— • ————————————
2n - 7 n2 • (n + 8)
STEP
12
:
Canceling Out
12.1 Cancel out (2n-7) which appears on both sides of the fraction line.
Canceling Out :
12.2 Canceling out n2 as it appears on both sides of the fraction line
Final result :
6
—————
n + 8