Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(7a2 + 53a) + 28
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 7a2+53a+28
The first term is, 7a2 its coefficient is 7 .
The middle term is, +53a its coefficient is 53 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 7 • 28 = 196
Step-2 : Find two factors of 196 whose sum equals the coefficient of the middle term, which is 53 .
| -196 | + | -1 | = | -197 | ||
| -98 | + | -2 | = | -100 | ||
| -49 | + | -4 | = | -53 | ||
| -28 | + | -7 | = | -35 | ||
| -14 | + | -14 | = | -28 | ||
| -7 | + | -28 | = | -35 | ||
| -4 | + | -49 | = | -53 | ||
| -2 | + | -98 | = | -100 | ||
| -1 | + | -196 | = | -197 | ||
| 1 | + | 196 | = | 197 | ||
| 2 | + | 98 | = | 100 | ||
| 4 | + | 49 | = | 53 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 49
7a2 + 4a + 49a + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
a • (7a+4)
Add up the last 2 terms, pulling out common factors :
7 • (7a+4)
Step-5 : Add up the four terms of step 4 :
(a+7) • (7a+4)
Which is the desired factorization
Final result :
(7a + 4) • (a + 7)
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