Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23x2 - 2x) - 45
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 8x2-2x-45
The first term is, 8x2 its coefficient is 8 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -45
Step-1 : Multiply the coefficient of the first term by the constant 8 • -45 = -360
Step-2 : Find two factors of -360 whose sum equals the coefficient of the middle term, which is -2 .
| -360 | + | 1 | = | -359 | ||
| -180 | + | 2 | = | -178 | ||
| -120 | + | 3 | = | -117 | ||
| -90 | + | 4 | = | -86 | ||
| -72 | + | 5 | = | -67 | ||
| -60 | + | 6 | = | -54 | ||
| -45 | + | 8 | = | -37 | ||
| -40 | + | 9 | = | -31 | ||
| -36 | + | 10 | = | -26 | ||
| -30 | + | 12 | = | -18 | ||
| -24 | + | 15 | = | -9 | ||
| -20 | + | 18 | = | -2 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 18
8x2 - 20x + 18x - 45
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-5)
Add up the last 2 terms, pulling out common factors :
9 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(4x+9) • (2x-5)
Which is the desired factorization
Final result :
(2x - 5) • (4x + 9)
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