Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(2x2 + 15x) + 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+15x+7
The first term is, 2x2 its coefficient is 2 .
The middle term is, +15x its coefficient is 15 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14
Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is 15 .
| -14 | + | -1 | = | -15 | ||
| -7 | + | -2 | = | -9 | ||
| -2 | + | -7 | = | -9 | ||
| -1 | + | -14 | = | -15 | ||
| 1 | + | 14 | = | 15 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 14
2x2 + 1x + 14x + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (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 :
(x+7) • (2x+1)
Which is the desired factorization
Final result :
(2x + 1) • (x + 7)
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