Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•5x2) + 7x) - 6
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 20x2+7x-6
The first term is, 20x2 its coefficient is 20 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 20 • -6 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is 7 .
| -120 | + | 1 | = | -119 | ||
| -60 | + | 2 | = | -58 | ||
| -40 | + | 3 | = | -37 | ||
| -30 | + | 4 | = | -26 | ||
| -24 | + | 5 | = | -19 | ||
| -20 | + | 6 | = | -14 | ||
| -15 | + | 8 | = | -7 | ||
| -12 | + | 10 | = | -2 | ||
| -10 | + | 12 | = | 2 | ||
| -8 | + | 15 | = | 7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 15
20x2 - 8x + 15x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (5x-2)
Add up the last 2 terms, pulling out common factors :
3 • (5x-2)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (5x-2)
Which is the desired factorization
Final result :
(5x - 2) • (4x + 3)
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