Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((24•3n2) - 56n) - 40
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
48n2 - 56n - 40 = 8 • (6n2 - 7n - 5)
Trying to factor by splitting the middle term
3.2 Factoring 6n2 - 7n - 5
The first term is, 6n2 its coefficient is 6 .
The middle term is, -7n its coefficient is -7 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 6 • -5 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -7 .
-30 | + | 1 | = | -29 | ||
-15 | + | 2 | = | -13 | ||
-10 | + | 3 | = | -7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 3
6n2 - 10n + 3n - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
2n • (3n-5)
Add up the last 2 terms, pulling out common factors :
1 • (3n-5)
Step-5 : Add up the four terms of step 4 :
(2n+1) • (3n-5)
Which is the desired factorization
Final result :
8 • (3n - 5) • (2n + 1)
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