Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3x2) + 17x) - 14
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6x2+17x-14
The first term is, 6x2 its coefficient is 6 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 6 • -14 = -84
Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is 17 .
| -84 | + | 1 | = | -83 | ||
| -42 | + | 2 | = | -40 | ||
| -28 | + | 3 | = | -25 | ||
| -21 | + | 4 | = | -17 | ||
| -14 | + | 6 | = | -8 | ||
| -12 | + | 7 | = | -5 | ||
| -7 | + | 12 | = | 5 | ||
| -6 | + | 14 | = | 8 | ||
| -4 | + | 21 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 21
6x2 - 4x + 21x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-2)
Add up the last 2 terms, pulling out common factors :
7 • (3x-2)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (3x-2)
Which is the desired factorization
Final result :
(3x - 2) • (2x + 7)
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