Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 39x) + 28
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+39x+28
The first term is, 5x2 its coefficient is 5 .
The middle term is, +39x its coefficient is 39 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 5 • 28 = 140
Step-2 : Find two factors of 140 whose sum equals the coefficient of the middle term, which is 39 .
| -140 | + | -1 | = | -141 | ||
| -70 | + | -2 | = | -72 | ||
| -35 | + | -4 | = | -39 | ||
| -28 | + | -5 | = | -33 | ||
| -20 | + | -7 | = | -27 | ||
| -14 | + | -10 | = | -24 | ||
| -10 | + | -14 | = | -24 | ||
| -7 | + | -20 | = | -27 | ||
| -5 | + | -28 | = | -33 | ||
| -4 | + | -35 | = | -39 | ||
| -2 | + | -70 | = | -72 | ||
| -1 | + | -140 | = | -141 | ||
| 1 | + | 140 | = | 141 | ||
| 2 | + | 70 | = | 72 | ||
| 4 | + | 35 | = | 39 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 35
5x2 + 4x + 35x + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+4)
Add up the last 2 terms, pulling out common factors :
7 • (5x+4)
Step-5 : Add up the four terms of step 4 :
(x+7) • (5x+4)
Which is the desired factorization
Final result :
(5x + 4) • (x + 7)
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