Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 31x) - 45
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+31x-45
The first term is, 4x2 its coefficient is 4 .
The middle term is, +31x its coefficient is 31 .
The last term, "the constant", is -45
Step-1 : Multiply the coefficient of the first term by the constant 4 • -45 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is 31 .
| -180 | + | 1 | = | -179 | ||
| -90 | + | 2 | = | -88 | ||
| -60 | + | 3 | = | -57 | ||
| -45 | + | 4 | = | -41 | ||
| -36 | + | 5 | = | -31 | ||
| -30 | + | 6 | = | -24 | ||
| -20 | + | 9 | = | -11 | ||
| -18 | + | 10 | = | -8 | ||
| -15 | + | 12 | = | -3 | ||
| -12 | + | 15 | = | 3 | ||
| -10 | + | 18 | = | 8 | ||
| -9 | + | 20 | = | 11 | ||
| -6 | + | 30 | = | 24 | ||
| -5 | + | 36 | = | 31 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 36
4x2 - 5x + 36x - 45
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x-5)
Add up the last 2 terms, pulling out common factors :
9 • (4x-5)
Step-5 : Add up the four terms of step 4 :
(x+9) • (4x-5)
Which is the desired factorization
Final result :
(4x - 5) • (x + 9)
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