Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(-x - 6) + (3•5x2)
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2-x-6
The first term is, 15x2 its coefficient is 15 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 15 • -6 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -1 .
| -90 | + | 1 | = | -89 | ||
| -45 | + | 2 | = | -43 | ||
| -30 | + | 3 | = | -27 | ||
| -18 | + | 5 | = | -13 | ||
| -15 | + | 6 | = | -9 | ||
| -10 | + | 9 | = | -1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 9
15x2 - 10x + 9x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (3x-2)
Add up the last 2 terms, pulling out common factors :
3 • (3x-2)
Step-5 : Add up the four terms of step 4 :
(5x+3) • (3x-2)
Which is the desired factorization
Final result :
(3x - 2) • (5x + 3)
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