Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•32x2) + 93x) - 8
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 36x2+93x-8
The first term is, 36x2 its coefficient is 36 .
The middle term is, +93x its coefficient is 93 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 36 • -8 = -288
Step-2 : Find two factors of -288 whose sum equals the coefficient of the middle term, which is 93 .
| -288 | + | 1 | = | -287 | ||
| -144 | + | 2 | = | -142 | ||
| -96 | + | 3 | = | -93 | ||
| -72 | + | 4 | = | -68 | ||
| -48 | + | 6 | = | -42 | ||
| -36 | + | 8 | = | -28 | ||
| -32 | + | 9 | = | -23 | ||
| -24 | + | 12 | = | -12 | ||
| -18 | + | 16 | = | -2 | ||
| -16 | + | 18 | = | 2 | ||
| -12 | + | 24 | = | 12 | ||
| -9 | + | 32 | = | 23 | ||
| -8 | + | 36 | = | 28 | ||
| -6 | + | 48 | = | 42 | ||
| -4 | + | 72 | = | 68 | ||
| -3 | + | 96 | = | 93 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 96
36x2 - 3x + 96x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (12x-1)
Add up the last 2 terms, pulling out common factors :
8 • (12x-1)
Step-5 : Add up the four terms of step 4 :
(3x+8) • (12x-1)
Which is the desired factorization
Final result :
(12x - 1) • (3x + 8)
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