Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•7x2) + 13x) - 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 21x2+13x-20
The first term is, 21x2 its coefficient is 21 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 21 • -20 = -420
Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is 13 .
| -420 | + | 1 | = | -419 | ||
| -210 | + | 2 | = | -208 | ||
| -140 | + | 3 | = | -137 | ||
| -105 | + | 4 | = | -101 | ||
| -84 | + | 5 | = | -79 | ||
| -70 | + | 6 | = | -64 | ||
| -60 | + | 7 | = | -53 | ||
| -42 | + | 10 | = | -32 | ||
| -35 | + | 12 | = | -23 | ||
| -30 | + | 14 | = | -16 | ||
| -28 | + | 15 | = | -13 | ||
| -21 | + | 20 | = | -1 | ||
| -20 | + | 21 | = | 1 | ||
| -15 | + | 28 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 28
21x2 - 15x + 28x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (7x-5)
Add up the last 2 terms, pulling out common factors :
4 • (7x-5)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (7x-5)
Which is the desired factorization
Final result :
(7x - 5) • (3x + 4)
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