Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23x2 - 22x) + 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 8x2-22x+15
The first term is, 8x2 its coefficient is 8 .
The middle term is, -22x its coefficient is -22 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 8 • 15 = 120
Step-2 : Find two factors of 120 whose sum equals the coefficient of the middle term, which is -22 .
| -120 | + | -1 | = | -121 | ||
| -60 | + | -2 | = | -62 | ||
| -40 | + | -3 | = | -43 | ||
| -30 | + | -4 | = | -34 | ||
| -24 | + | -5 | = | -29 | ||
| -20 | + | -6 | = | -26 | ||
| -15 | + | -8 | = | -23 | ||
| -12 | + | -10 | = | -22 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -10
8x2 - 12x - 10x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-3)
Add up the last 2 terms, pulling out common factors :
5 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(4x-5) • (2x-3)
Which is the desired factorization
Final result :
(2x - 3) • (4x - 5)
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