Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(7x2 + 38x) - 24
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 7x2+38x-24
The first term is, 7x2 its coefficient is 7 .
The middle term is, +38x its coefficient is 38 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 7 • -24 = -168
Step-2 : Find two factors of -168 whose sum equals the coefficient of the middle term, which is 38 .
| -168 | + | 1 | = | -167 | ||
| -84 | + | 2 | = | -82 | ||
| -56 | + | 3 | = | -53 | ||
| -42 | + | 4 | = | -38 | ||
| -28 | + | 6 | = | -22 | ||
| -24 | + | 7 | = | -17 | ||
| -21 | + | 8 | = | -13 | ||
| -14 | + | 12 | = | -2 | ||
| -12 | + | 14 | = | 2 | ||
| -8 | + | 21 | = | 13 | ||
| -7 | + | 24 | = | 17 | ||
| -6 | + | 28 | = | 22 | ||
| -4 | + | 42 | = | 38 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 42
7x2 - 4x + 42x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (7x-4)
Add up the last 2 terms, pulling out common factors :
6 • (7x-4)
Step-5 : Add up the four terms of step 4 :
(x+6) • (7x-4)
Which is the desired factorization
Final result :
(7x - 4) • (x + 6)
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