Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(10a + 7) - 23a2
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring -8a2+10a+7
The first term is, -8a2 its coefficient is -8 .
The middle term is, +10a 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
-8a2 - 4a + 14a + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
-4a • (2a+1)
Add up the last 2 terms, pulling out common factors :
7 • (2a+1)
Step-5 : Add up the four terms of step 4 :
(-4a+7) • (2a+1)
Which is the desired factorization
Final result :
(2a + 1) • (7 - 4a)
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