Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((32•11q2) - 74q) - 40
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 99q2-74q-40
The first term is, 99q2 its coefficient is 99 .
The middle term is, -74q its coefficient is -74 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 99 • -40 = -3960
Step-2 : Find two factors of -3960 whose sum equals the coefficient of the middle term, which is -74 .
| -3960 | + | 1 | = | -3959 | ||
| -1980 | + | 2 | = | -1978 | ||
| -1320 | + | 3 | = | -1317 | ||
| -990 | + | 4 | = | -986 | ||
| -792 | + | 5 | = | -787 | ||
| -660 | + | 6 | = | -654 | ||
| -495 | + | 8 | = | -487 | ||
| -440 | + | 9 | = | -431 | ||
| -396 | + | 10 | = | -386 | ||
| -360 | + | 11 | = | -349 | ||
| -330 | + | 12 | = | -318 | ||
| -264 | + | 15 | = | -249 | ||
| -220 | + | 18 | = | -202 | ||
| -198 | + | 20 | = | -178 | ||
| -180 | + | 22 | = | -158 | ||
| -165 | + | 24 | = | -141 | ||
| -132 | + | 30 | = | -102 | ||
| -120 | + | 33 | = | -87 | ||
| -110 | + | 36 | = | -74 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -110 and 36
99q2 - 110q + 36q - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
11q • (9q-10)
Add up the last 2 terms, pulling out common factors :
4 • (9q-10)
Step-5 : Add up the four terms of step 4 :
(11q+4) • (9q-10)
Which is the desired factorization
Final result :
(9q - 10) • (11q + 4)
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