Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•5n2) + 44n) - 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 20n2+44n-15
The first term is, 20n2 its coefficient is 20 .
The middle term is, +44n its coefficient is 44 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 20 • -15 = -300
Step-2 : Find two factors of -300 whose sum equals the coefficient of the middle term, which is 44 .
| -300 | + | 1 | = | -299 | ||
| -150 | + | 2 | = | -148 | ||
| -100 | + | 3 | = | -97 | ||
| -75 | + | 4 | = | -71 | ||
| -60 | + | 5 | = | -55 | ||
| -50 | + | 6 | = | -44 | ||
| -30 | + | 10 | = | -20 | ||
| -25 | + | 12 | = | -13 | ||
| -20 | + | 15 | = | -5 | ||
| -15 | + | 20 | = | 5 | ||
| -12 | + | 25 | = | 13 | ||
| -10 | + | 30 | = | 20 | ||
| -6 | + | 50 | = | 44 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 50
20n2 - 6n + 50n - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2n • (10n-3)
Add up the last 2 terms, pulling out common factors :
5 • (10n-3)
Step-5 : Add up the four terms of step 4 :
(2n+5) • (10n-3)
Which is the desired factorization
Final result :
(10n - 3) • (2n + 5)
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