Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•5x2) - 39x) + 18
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 20x2-39x+18
The first term is, 20x2 its coefficient is 20 .
The middle term is, -39x its coefficient is -39 .
The last term, "the constant", is +18
Step-1 : Multiply the coefficient of the first term by the constant 20 • 18 = 360
Step-2 : Find two factors of 360 whose sum equals the coefficient of the middle term, which is -39 .
| -360 | + | -1 | = | -361 | ||
| -180 | + | -2 | = | -182 | ||
| -120 | + | -3 | = | -123 | ||
| -90 | + | -4 | = | -94 | ||
| -72 | + | -5 | = | -77 | ||
| -60 | + | -6 | = | -66 | ||
| -45 | + | -8 | = | -53 | ||
| -40 | + | -9 | = | -49 | ||
| -36 | + | -10 | = | -46 | ||
| -30 | + | -12 | = | -42 | ||
| -24 | + | -15 | = | -39 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and -15
20x2 - 24x - 15x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (5x-6)
Add up the last 2 terms, pulling out common factors :
3 • (5x-6)
Step-5 : Add up the four terms of step 4 :
(4x-3) • (5x-6)
Which is the desired factorization
Final result :
(5x - 6) • (4x - 3)
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