Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23m2 + 30m) + 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 8m2+30m+7
The first term is, 8m2 its coefficient is 8 .
The middle term is, +30m its coefficient is 30 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 8 • 7 = 56
Step-2 : Find two factors of 56 whose sum equals the coefficient of the middle term, which is 30 .
| -56 | + | -1 | = | -57 | ||
| -28 | + | -2 | = | -30 | ||
| -14 | + | -4 | = | -18 | ||
| -8 | + | -7 | = | -15 | ||
| -7 | + | -8 | = | -15 | ||
| -4 | + | -14 | = | -18 | ||
| -2 | + | -28 | = | -30 | ||
| -1 | + | -56 | = | -57 | ||
| 1 | + | 56 | = | 57 | ||
| 2 | + | 28 | = | 30 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 28
8m2 + 2m + 28m + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
2m • (4m+1)
Add up the last 2 terms, pulling out common factors :
7 • (4m+1)
Step-5 : Add up the four terms of step 4 :
(2m+7) • (4m+1)
Which is the desired factorization
Final result :
(4m + 1) • (2m + 7)
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