Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3x2) + x) - 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6x2+x-12
The first term is, 6x2 its coefficient is 6 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 6 • -12 = -72
Step-2 : Find two factors of -72 whose sum equals the coefficient of the middle term, which is 1 .
| -72 | + | 1 | = | -71 | ||
| -36 | + | 2 | = | -34 | ||
| -24 | + | 3 | = | -21 | ||
| -18 | + | 4 | = | -14 | ||
| -12 | + | 6 | = | -6 | ||
| -9 | + | 8 | = | -1 | ||
| -8 | + | 9 | = | 1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 9
6x2 - 8x + 9x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-4)
Add up the last 2 terms, pulling out common factors :
3 • (3x-4)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (3x-4)
Which is the desired factorization
Final result :
(3x - 4) • (2x + 3)
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