Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+18x+80
The first term is, x2 its coefficient is 1 .
The middle term is, +18x its coefficient is 18 .
The last term, "the constant", is +80
Step-1 : Multiply the coefficient of the first term by the constant 1 • 80 = 80
Step-2 : Find two factors of 80 whose sum equals the coefficient of the middle term, which is 18 .
| -80 | + | -1 | = | -81 | ||
| -40 | + | -2 | = | -42 | ||
| -20 | + | -4 | = | -24 | ||
| -16 | + | -5 | = | -21 | ||
| -10 | + | -8 | = | -18 | ||
| -8 | + | -10 | = | -18 | ||
| -5 | + | -16 | = | -21 | ||
| -4 | + | -20 | = | -24 | ||
| -2 | + | -40 | = | -42 | ||
| -1 | + | -80 | = | -81 | ||
| 1 | + | 80 | = | 81 | ||
| 2 | + | 40 | = | 42 | ||
| 4 | + | 20 | = | 24 | ||
| 5 | + | 16 | = | 21 | ||
| 8 | + | 10 | = | 18 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 10
x2 + 8x + 10x + 80
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+8)
Add up the last 2 terms, pulling out common factors :
10 • (x+8)
Step-5 : Add up the four terms of step 4 :
(x+10) • (x+8)
Which is the desired factorization
Final result :
(x + 10) • (x + 8)
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