Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(25x2 + 40x) - 28
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
32x2 + 40x - 28 = 4 • (8x2 + 10x - 7)
Trying to factor by splitting the middle term
3.2 Factoring 8x2 + 10x - 7
The first term is, 8x2 its coefficient is 8 .
The middle term is, +10x its coefficient is 10 .
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 10 .
| -56 | + | 1 | = | -55 | ||
| -28 | + | 2 | = | -26 | ||
| -14 | + | 4 | = | -10 | ||
| -8 | + | 7 | = | -1 | ||
| -7 | + | 8 | = | 1 | ||
| -4 | + | 14 | = | 10 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 14
8x2 - 4x + 14x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-1)
Add up the last 2 terms, pulling out common factors :
7 • (2x-1)
Step-5 : Add up the four terms of step 4 :
(4x+7) • (2x-1)
Which is the desired factorization
Final result :
4 • (2x - 1) • (4x + 7)
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