Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23v2 + 26v) - 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 8v2+26v-7
The first term is, 8v2 its coefficient is 8 .
The middle term is, +26v its coefficient is 26 .
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 26 .
| -56 | + | 1 | = | -55 | ||
| -28 | + | 2 | = | -26 | ||
| -14 | + | 4 | = | -10 | ||
| -8 | + | 7 | = | -1 | ||
| -7 | + | 8 | = | 1 | ||
| -4 | + | 14 | = | 10 | ||
| -2 | + | 28 | = | 26 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 28
8v2 - 2v + 28v - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
2v • (4v-1)
Add up the last 2 terms, pulling out common factors :
7 • (4v-1)
Step-5 : Add up the four terms of step 4 :
(2v+7) • (4v-1)
Which is the desired factorization
Final result :
(4v - 1) • (2v + 7)
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