Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - 2x2) - 17x) - 30
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-2x2 - 17x - 30 = -1 • (2x2 + 17x + 30)
Trying to factor by splitting the middle term
3.2 Factoring 2x2 + 17x + 30
The first term is, 2x2 its coefficient is 2 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is +30
Step-1 : Multiply the coefficient of the first term by the constant 2 • 30 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is 17 .
| -60 | + | -1 | = | -61 | ||
| -30 | + | -2 | = | -32 | ||
| -20 | + | -3 | = | -23 | ||
| -15 | + | -4 | = | -19 | ||
| -12 | + | -5 | = | -17 | ||
| -10 | + | -6 | = | -16 | ||
| -6 | + | -10 | = | -16 | ||
| -5 | + | -12 | = | -17 | ||
| -4 | + | -15 | = | -19 | ||
| -3 | + | -20 | = | -23 | ||
| -2 | + | -30 | = | -32 | ||
| -1 | + | -60 | = | -61 | ||
| 1 | + | 60 | = | 61 | ||
| 2 | + | 30 | = | 32 | ||
| 3 | + | 20 | = | 23 | ||
| 4 | + | 15 | = | 19 | ||
| 5 | + | 12 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 12
2x2 + 5x + 12x + 30
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+5)
Add up the last 2 terms, pulling out common factors :
6 • (2x+5)
Step-5 : Add up the four terms of step 4 :
(x+6) • (2x+5)
Which is the desired factorization
Final result :
(-2x - 5) • (x + 6)
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