Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5m2) + 11m) - 14
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15m2+11m-14
The first term is, 15m2 its coefficient is 15 .
The middle term is, +11m its coefficient is 11 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 15 • -14 = -210
Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is 11 .
| -210 | + | 1 | = | -209 | ||
| -105 | + | 2 | = | -103 | ||
| -70 | + | 3 | = | -67 | ||
| -42 | + | 5 | = | -37 | ||
| -35 | + | 6 | = | -29 | ||
| -30 | + | 7 | = | -23 | ||
| -21 | + | 10 | = | -11 | ||
| -15 | + | 14 | = | -1 | ||
| -14 | + | 15 | = | 1 | ||
| -10 | + | 21 | = | 11 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 21
15m2 - 10m + 21m - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
5m • (3m-2)
Add up the last 2 terms, pulling out common factors :
7 • (3m-2)
Step-5 : Add up the four terms of step 4 :
(5m+7) • (3m-2)
Which is the desired factorization
Final result :
(3m - 2) • (5m + 7)
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