Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(32p2 + 6p) - 8
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 9p2+6p-8
The first term is, 9p2 its coefficient is 9 .
The middle term is, +6p its coefficient is 6 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 9 • -8 = -72
Step-2 : Find two factors of -72 whose sum equals the coefficient of the middle term, which is 6 .
| -72 | + | 1 | = | -71 | ||
| -36 | + | 2 | = | -34 | ||
| -24 | + | 3 | = | -21 | ||
| -18 | + | 4 | = | -14 | ||
| -12 | + | 6 | = | -6 | ||
| -9 | + | 8 | = | -1 | ||
| -8 | + | 9 | = | 1 | ||
| -6 | + | 12 | = | 6 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 12
9p2 - 6p + 12p - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
3p • (3p-2)
Add up the last 2 terms, pulling out common factors :
4 • (3p-2)
Step-5 : Add up the four terms of step 4 :
(3p+4) • (3p-2)
Which is the desired factorization
Final result :
(3p - 2) • (3p + 4)
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