Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(32a2 - 42a) + 40
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 9a2-42a+40
The first term is, 9a2 its coefficient is 9 .
The middle term is, -42a its coefficient is -42 .
The last term, "the constant", is +40
Step-1 : Multiply the coefficient of the first term by the constant 9 • 40 = 360
Step-2 : Find two factors of 360 whose sum equals the coefficient of the middle term, which is -42 .
| -360 | + | -1 | = | -361 | ||
| -180 | + | -2 | = | -182 | ||
| -120 | + | -3 | = | -123 | ||
| -90 | + | -4 | = | -94 | ||
| -72 | + | -5 | = | -77 | ||
| -60 | + | -6 | = | -66 | ||
| -45 | + | -8 | = | -53 | ||
| -40 | + | -9 | = | -49 | ||
| -36 | + | -10 | = | -46 | ||
| -30 | + | -12 | = | -42 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -30 and -12
9a2 - 30a - 12a - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
3a • (3a-10)
Add up the last 2 terms, pulling out common factors :
4 • (3a-10)
Step-5 : Add up the four terms of step 4 :
(3a-4) • (3a-10)
Which is the desired factorization
Final result :
(3a - 10) • (3a - 4)
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