Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•5x2) - 9x) - 36
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 10x2-9x-36
The first term is, 10x2 its coefficient is 10 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 10 • -36 = -360
Step-2 : Find two factors of -360 whose sum equals the coefficient of the middle term, which is -9 .
| -360 | + | 1 | = | -359 | ||
| -180 | + | 2 | = | -178 | ||
| -120 | + | 3 | = | -117 | ||
| -90 | + | 4 | = | -86 | ||
| -72 | + | 5 | = | -67 | ||
| -60 | + | 6 | = | -54 | ||
| -45 | + | 8 | = | -37 | ||
| -40 | + | 9 | = | -31 | ||
| -36 | + | 10 | = | -26 | ||
| -30 | + | 12 | = | -18 | ||
| -24 | + | 15 | = | -9 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and 15
10x2 - 24x + 15x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (5x-12)
Add up the last 2 terms, pulling out common factors :
3 • (5x-12)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (5x-12)
Which is the desired factorization
Final result :
(5x - 12) • (2x + 3)
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