Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(2x2 + 17x) + 35
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+17x+35
The first term is, 2x2 its coefficient is 2 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is +35
Step-1 : Multiply the coefficient of the first term by the constant 2 • 35 = 70
Step-2 : Find two factors of 70 whose sum equals the coefficient of the middle term, which is 17 .
| -70 | + | -1 | = | -71 | ||
| -35 | + | -2 | = | -37 | ||
| -14 | + | -5 | = | -19 | ||
| -10 | + | -7 | = | -17 | ||
| -7 | + | -10 | = | -17 | ||
| -5 | + | -14 | = | -19 | ||
| -2 | + | -35 | = | -37 | ||
| -1 | + | -70 | = | -71 | ||
| 1 | + | 70 | = | 71 | ||
| 2 | + | 35 | = | 37 | ||
| 5 | + | 14 | = | 19 | ||
| 7 | + | 10 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 10
2x2 + 7x + 10x + 35
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+7)
Add up the last 2 terms, pulling out common factors :
5 • (2x+7)
Step-5 : Add up the four terms of step 4 :
(x+5) • (2x+7)
Which is the desired factorization
Final result :
(2x + 7) • (x + 5)
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