Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((23•32w2) + 35w) + 3
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 72w2+35w+3
The first term is, 72w2 its coefficient is 72 .
The middle term is, +35w its coefficient is 35 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 72 • 3 = 216
Step-2 : Find two factors of 216 whose sum equals the coefficient of the middle term, which is 35 .
| -216 | + | -1 | = | -217 | ||
| -108 | + | -2 | = | -110 | ||
| -72 | + | -3 | = | -75 | ||
| -54 | + | -4 | = | -58 | ||
| -36 | + | -6 | = | -42 | ||
| -27 | + | -8 | = | -35 | ||
| -24 | + | -9 | = | -33 | ||
| -18 | + | -12 | = | -30 | ||
| -12 | + | -18 | = | -30 | ||
| -9 | + | -24 | = | -33 | ||
| -8 | + | -27 | = | -35 | ||
| -6 | + | -36 | = | -42 | ||
| -4 | + | -54 | = | -58 | ||
| -3 | + | -72 | = | -75 | ||
| -2 | + | -108 | = | -110 | ||
| -1 | + | -216 | = | -217 | ||
| 1 | + | 216 | = | 217 | ||
| 2 | + | 108 | = | 110 | ||
| 3 | + | 72 | = | 75 | ||
| 4 | + | 54 | = | 58 | ||
| 6 | + | 36 | = | 42 | ||
| 8 | + | 27 | = | 35 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 27
72w2 + 8w + 27w + 3
Step-4 : Add up the first 2 terms, pulling out like factors :
8w • (9w+1)
Add up the last 2 terms, pulling out common factors :
3 • (9w+1)
Step-5 : Add up the four terms of step 4 :
(8w+3) • (9w+1)
Which is the desired factorization
Final result :
(9w + 1) • (8w + 3)
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