Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 13x) - 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+13x-10
The first term is, 3x2 its coefficient is 3 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 3 • -10 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is 13 .
| -30 | + | 1 | = | -29 | ||
| -15 | + | 2 | = | -13 | ||
| -10 | + | 3 | = | -7 | ||
| -6 | + | 5 | = | -1 | ||
| -5 | + | 6 | = | 1 | ||
| -3 | + | 10 | = | 7 | ||
| -2 | + | 15 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 15
3x2 - 2x + 15x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (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 :
(x+5) • (3x-2)
Which is the desired factorization
Final result :
(3x - 2) • (x + 5)
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