Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•32p2) + 114p) - 20
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
36p2 + 114p - 20 = 2 • (18p2 + 57p - 10)
Trying to factor by splitting the middle term
3.2 Factoring 18p2 + 57p - 10
The first term is, 18p2 its coefficient is 18 .
The middle term is, +57p its coefficient is 57 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 18 • -10 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is 57 .
| -180 | + | 1 | = | -179 | ||
| -90 | + | 2 | = | -88 | ||
| -60 | + | 3 | = | -57 | ||
| -45 | + | 4 | = | -41 | ||
| -36 | + | 5 | = | -31 | ||
| -30 | + | 6 | = | -24 | ||
| -20 | + | 9 | = | -11 | ||
| -18 | + | 10 | = | -8 | ||
| -15 | + | 12 | = | -3 | ||
| -12 | + | 15 | = | 3 | ||
| -10 | + | 18 | = | 8 | ||
| -9 | + | 20 | = | 11 | ||
| -6 | + | 30 | = | 24 | ||
| -5 | + | 36 | = | 31 | ||
| -4 | + | 45 | = | 41 | ||
| -3 | + | 60 | = | 57 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 60
18p2 - 3p + 60p - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
3p • (6p-1)
Add up the last 2 terms, pulling out common factors :
10 • (6p-1)
Step-5 : Add up the four terms of step 4 :
(3p+10) • (6p-1)
Which is the desired factorization
Final result :
2 • (6p - 1) • (3p + 10)
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