Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+13x+40
The first term is, x2 its coefficient is 1 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +40
Step-1 : Multiply the coefficient of the first term by the constant 1 • 40 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is 13 .
| -40 | + | -1 | = | -41 | ||
| -20 | + | -2 | = | -22 | ||
| -10 | + | -4 | = | -14 | ||
| -8 | + | -5 | = | -13 | ||
| -5 | + | -8 | = | -13 | ||
| -4 | + | -10 | = | -14 | ||
| -2 | + | -20 | = | -22 | ||
| -1 | + | -40 | = | -41 | ||
| 1 | + | 40 | = | 41 | ||
| 2 | + | 20 | = | 22 | ||
| 4 | + | 10 | = | 14 | ||
| 5 | + | 8 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 8
x2 + 5x + 8x + 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+5)
Add up the last 2 terms, pulling out common factors :
8 • (x+5)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x+5)
Which is the desired factorization
Final result :
(x + 8) • (x + 5)
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