Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•3x2) + 17x) + 6
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 12x2+17x+6
The first term is, 12x2 its coefficient is 12 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 12 • 6 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 17 .
| -72 | + | -1 | = | -73 | ||
| -36 | + | -2 | = | -38 | ||
| -24 | + | -3 | = | -27 | ||
| -18 | + | -4 | = | -22 | ||
| -12 | + | -6 | = | -18 | ||
| -9 | + | -8 | = | -17 | ||
| -8 | + | -9 | = | -17 | ||
| -6 | + | -12 | = | -18 | ||
| -4 | + | -18 | = | -22 | ||
| -3 | + | -24 | = | -27 | ||
| -2 | + | -36 | = | -38 | ||
| -1 | + | -72 | = | -73 | ||
| 1 | + | 72 | = | 73 | ||
| 2 | + | 36 | = | 38 | ||
| 3 | + | 24 | = | 27 | ||
| 4 | + | 18 | = | 22 | ||
| 6 | + | 12 | = | 18 | ||
| 8 | + | 9 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 9
12x2 + 8x + 9x + 6
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (3x+2)
Add up the last 2 terms, pulling out common factors :
3 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (3x+2)
Which is the desired factorization
Final result :
(3x + 2) • (4x + 3)
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