Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+15x+56
The first term is, x2 its coefficient is 1 .
The middle term is, +15x its coefficient is 15 .
The last term, "the constant", is +56
Step-1 : Multiply the coefficient of the first term by the constant 1 • 56 = 56
Step-2 : Find two factors of 56 whose sum equals the coefficient of the middle term, which is 15 .
| -56 | + | -1 | = | -57 | ||
| -28 | + | -2 | = | -30 | ||
| -14 | + | -4 | = | -18 | ||
| -8 | + | -7 | = | -15 | ||
| -7 | + | -8 | = | -15 | ||
| -4 | + | -14 | = | -18 | ||
| -2 | + | -28 | = | -30 | ||
| -1 | + | -56 | = | -57 | ||
| 1 | + | 56 | = | 57 | ||
| 2 | + | 28 | = | 30 | ||
| 4 | + | 14 | = | 18 | ||
| 7 | + | 8 | = | 15 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 8
x2 + 7x + 8x + 56
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+7)
Add up the last 2 terms, pulling out common factors :
8 • (x+7)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x+7)
Which is the desired factorization
Final result :
(x + 8) • (x + 7)
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