Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 12x) + 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+12x+7
The first term is, 5x2 its coefficient is 5 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 5 • 7 = 35
Step-2 : Find two factors of 35 whose sum equals the coefficient of the middle term, which is 12 .
| -35 | + | -1 | = | -36 | ||
| -7 | + | -5 | = | -12 | ||
| -5 | + | -7 | = | -12 | ||
| -1 | + | -35 | = | -36 | ||
| 1 | + | 35 | = | 36 | ||
| 5 | + | 7 | = | 12 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 7
5x2 + 5x + 7x + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x+1)
Add up the last 2 terms, pulling out common factors :
7 • (x+1)
Step-5 : Add up the four terms of step 4 :
(5x+7) • (x+1)
Which is the desired factorization
Final result :
(x + 1) • (5x + 7)
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