Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3x2) + 11x) - 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6x2+11x-10
The first term is, 6x2 its coefficient is 6 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 6 • -10 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is 11 .
| -60 | + | 1 | = | -59 | ||
| -30 | + | 2 | = | -28 | ||
| -20 | + | 3 | = | -17 | ||
| -15 | + | 4 | = | -11 | ||
| -12 | + | 5 | = | -7 | ||
| -10 | + | 6 | = | -4 | ||
| -6 | + | 10 | = | 4 | ||
| -5 | + | 12 | = | 7 | ||
| -4 | + | 15 | = | 11 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 15
6x2 - 4x + 15x - 10
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 :
5 • (3x-2)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (3x-2)
Which is the desired factorization
Final result :
(3x - 2) • (2x + 5)
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