Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+241n-18060
The first term is, n2 its coefficient is 1 .
The middle term is, +241n its coefficient is 241 .
The last term, "the constant", is -18060
Step-1 : Multiply the coefficient of the first term by the constant 1 • -18060 = -18060
Step-2 : Find two factors of -18060 whose sum equals the coefficient of the middle term, which is 241 .
| -18060 | + | 1 | = | -18059 | ||
| -9030 | + | 2 | = | -9028 | ||
| -6020 | + | 3 | = | -6017 | ||
| -4515 | + | 4 | = | -4511 | ||
| -3612 | + | 5 | = | -3607 | ||
| -3010 | + | 6 | = | -3004 | ||
| -2580 | + | 7 | = | -2573 | ||
| -1806 | + | 10 | = | -1796 | ||
| -1505 | + | 12 | = | -1493 | ||
| -1290 | + | 14 | = | -1276 | ||
| -1204 | + | 15 | = | -1189 | ||
| -903 | + | 20 | = | -883 | ||
| -860 | + | 21 | = | -839 | ||
| -645 | + | 28 | = | -617 | ||
| -602 | + | 30 | = | -572 | ||
| -516 | + | 35 | = | -481 | ||
| -430 | + | 42 | = | -388 | ||
| -420 | + | 43 | = | -377 | ||
| -301 | + | 60 | = | -241 | ||
| -258 | + | 70 | = | -188 | ||
| -215 | + | 84 | = | -131 | ||
| -210 | + | 86 | = | -124 | ||
| -172 | + | 105 | = | -67 | ||
| -140 | + | 129 | = | -11 | ||
| -129 | + | 140 | = | 11 | ||
| -105 | + | 172 | = | 67 | ||
| -86 | + | 210 | = | 124 | ||
| -84 | + | 215 | = | 131 | ||
| -70 | + | 258 | = | 188 | ||
| -60 | + | 301 | = | 241 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -60 and 301
n2 - 60n + 301n - 18060
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n-60)
Add up the last 2 terms, pulling out common factors :
301 • (n-60)
Step-5 : Add up the four terms of step 4 :
(n+301) • (n-60)
Which is the desired factorization
Final result :
(n + 301) • (n - 60)
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