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+44
The first term is, x2 its coefficient is 1 .
The middle term is, +15x its coefficient is 15 .
The last term, "the constant", is +44
Step-1 : Multiply the coefficient of the first term by the constant 1 • 44 = 44
Step-2 : Find two factors of 44 whose sum equals the coefficient of the middle term, which is 15 .
| -44 | + | -1 | = | -45 | ||
| -22 | + | -2 | = | -24 | ||
| -11 | + | -4 | = | -15 | ||
| -4 | + | -11 | = | -15 | ||
| -2 | + | -22 | = | -24 | ||
| -1 | + | -44 | = | -45 | ||
| 1 | + | 44 | = | 45 | ||
| 2 | + | 22 | = | 24 | ||
| 4 | + | 11 | = | 15 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 11
x2 + 4x + 11x + 44
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+4)
Add up the last 2 terms, pulling out common factors :
11 • (x+4)
Step-5 : Add up the four terms of step 4 :
(x+11) • (x+4)
Which is the desired factorization
Final result :
(x + 11) • (x + 4)
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