Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 17x) - 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+17x-15
The first term is, 4x2 its coefficient is 4 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 4 • -15 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is 17 .
| -60 | + | 1 | = | -59 | ||
| -30 | + | 2 | = | -28 | ||
| -20 | + | 3 | = | -17 | ||
| -15 | + | 4 | = | -11 | ||
| -12 | + | 5 | = | -7 | ||
| -10 | + | 6 | = | -4 | ||
| -6 | + | 10 | = | 4 | ||
| -5 | + | 12 | = | 7 | ||
| -4 | + | 15 | = | 11 | ||
| -3 | + | 20 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 20
4x2 - 3x + 20x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x-3)
Add up the last 2 terms, pulling out common factors :
5 • (4x-3)
Step-5 : Add up the four terms of step 4 :
(x+5) • (4x-3)
Which is the desired factorization
Final result :
(4x - 3) • (x + 5)
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