Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•3x2) + 29x) + 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 12x2+29x+15
The first term is, 12x2 its coefficient is 12 .
The middle term is, +29x its coefficient is 29 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 12 • 15 = 180
Step-2 : Find two factors of 180 whose sum equals the coefficient of the middle term, which is 29 .
| -180 | + | -1 | = | -181 | ||
| -90 | + | -2 | = | -92 | ||
| -60 | + | -3 | = | -63 | ||
| -45 | + | -4 | = | -49 | ||
| -36 | + | -5 | = | -41 | ||
| -30 | + | -6 | = | -36 | ||
| -20 | + | -9 | = | -29 | ||
| -18 | + | -10 | = | -28 | ||
| -15 | + | -12 | = | -27 | ||
| -12 | + | -15 | = | -27 | ||
| -10 | + | -18 | = | -28 | ||
| -9 | + | -20 | = | -29 | ||
| -6 | + | -30 | = | -36 | ||
| -5 | + | -36 | = | -41 | ||
| -4 | + | -45 | = | -49 | ||
| -3 | + | -60 | = | -63 | ||
| -2 | + | -90 | = | -92 | ||
| -1 | + | -180 | = | -181 | ||
| 1 | + | 180 | = | 181 | ||
| 2 | + | 90 | = | 92 | ||
| 3 | + | 60 | = | 63 | ||
| 4 | + | 45 | = | 49 | ||
| 5 | + | 36 | = | 41 | ||
| 6 | + | 30 | = | 36 | ||
| 9 | + | 20 | = | 29 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 9 and 20
12x2 + 9x + 20x + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (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 :
(3x+5) • (4x+3)
Which is the desired factorization
Final result :
(4x + 3) • (3x + 5)
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