Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+16n+63
The first term is, n2 its coefficient is 1 .
The middle term is, +16n its coefficient is 16 .
The last term, "the constant", is +63
Step-1 : Multiply the coefficient of the first term by the constant 1 • 63 = 63
Step-2 : Find two factors of 63 whose sum equals the coefficient of the middle term, which is 16 .
| -63 | + | -1 | = | -64 | ||
| -21 | + | -3 | = | -24 | ||
| -9 | + | -7 | = | -16 | ||
| -7 | + | -9 | = | -16 | ||
| -3 | + | -21 | = | -24 | ||
| -1 | + | -63 | = | -64 | ||
| 1 | + | 63 | = | 64 | ||
| 3 | + | 21 | = | 24 | ||
| 7 | + | 9 | = | 16 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 9
n2 + 7n + 9n + 63
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n+7)
Add up the last 2 terms, pulling out common factors :
9 • (n+7)
Step-5 : Add up the four terms of step 4 :
(n+9) • (n+7)
Which is the desired factorization
Final result :
(n + 9) • (n + 7)
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