Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+20x+99
The first term is, x2 its coefficient is 1 .
The middle term is, +20x its coefficient is 20 .
The last term, "the constant", is +99
Step-1 : Multiply the coefficient of the first term by the constant 1 • 99 = 99
Step-2 : Find two factors of 99 whose sum equals the coefficient of the middle term, which is 20 .
| -99 | + | -1 | = | -100 | ||
| -33 | + | -3 | = | -36 | ||
| -11 | + | -9 | = | -20 | ||
| -9 | + | -11 | = | -20 | ||
| -3 | + | -33 | = | -36 | ||
| -1 | + | -99 | = | -100 | ||
| 1 | + | 99 | = | 100 | ||
| 3 | + | 33 | = | 36 | ||
| 9 | + | 11 | = | 20 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 9 and 11
x2 + 9x + 11x + 99
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+9)
Add up the last 2 terms, pulling out common factors :
11 • (x+9)
Step-5 : Add up the four terms of step 4 :
(x+11) • (x+9)
Which is the desired factorization
Final result :
(x + 11) • (x + 9)
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