Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 11x) - 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+11x-12
The first term is, 15x2 its coefficient is 15 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 15 • -12 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is 11 .
| -180 | + | 1 | = | -179 | ||
| -90 | + | 2 | = | -88 | ||
| -60 | + | 3 | = | -57 | ||
| -45 | + | 4 | = | -41 | ||
| -36 | + | 5 | = | -31 | ||
| -30 | + | 6 | = | -24 | ||
| -20 | + | 9 | = | -11 | ||
| -18 | + | 10 | = | -8 | ||
| -15 | + | 12 | = | -3 | ||
| -12 | + | 15 | = | 3 | ||
| -10 | + | 18 | = | 8 | ||
| -9 | + | 20 | = | 11 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 20
15x2 - 9x + 20x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x-3)
Add up the last 2 terms, pulling out common factors :
4 • (5x-3)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (5x-3)
Which is the desired factorization
Final result :
(5x - 3) • (3x + 4)
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