Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+201n-5400
The first term is, n2 its coefficient is 1 .
The middle term is, +201n its coefficient is 201 .
The last term, "the constant", is -5400
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5400 = -5400
Step-2 : Find two factors of -5400 whose sum equals the coefficient of the middle term, which is 201 .
| -5400 | + | 1 | = | -5399 | ||
| -2700 | + | 2 | = | -2698 | ||
| -1800 | + | 3 | = | -1797 | ||
| -1350 | + | 4 | = | -1346 | ||
| -1080 | + | 5 | = | -1075 | ||
| -900 | + | 6 | = | -894 | ||
| -675 | + | 8 | = | -667 | ||
| -600 | + | 9 | = | -591 | ||
| -540 | + | 10 | = | -530 | ||
| -450 | + | 12 | = | -438 | ||
| -360 | + | 15 | = | -345 | ||
| -300 | + | 18 | = | -282 | ||
| -270 | + | 20 | = | -250 | ||
| -225 | + | 24 | = | -201 | ||
| -216 | + | 25 | = | -191 | ||
| -200 | + | 27 | = | -173 | ||
| -180 | + | 30 | = | -150 | ||
| -150 | + | 36 | = | -114 | ||
| -135 | + | 40 | = | -95 | ||
| -120 | + | 45 | = | -75 | ||
| -108 | + | 50 | = | -58 | ||
| -100 | + | 54 | = | -46 | ||
| -90 | + | 60 | = | -30 | ||
| -75 | + | 72 | = | -3 | ||
| -72 | + | 75 | = | 3 | ||
| -60 | + | 90 | = | 30 | ||
| -54 | + | 100 | = | 46 | ||
| -50 | + | 108 | = | 58 | ||
| -45 | + | 120 | = | 75 | ||
| -40 | + | 135 | = | 95 | ||
| -36 | + | 150 | = | 114 | ||
| -30 | + | 180 | = | 150 | ||
| -27 | + | 200 | = | 173 | ||
| -25 | + | 216 | = | 191 | ||
| -24 | + | 225 | = | 201 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and 225
n2 - 24n + 225n - 5400
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n-24)
Add up the last 2 terms, pulling out common factors :
225 • (n-24)
Step-5 : Add up the four terms of step 4 :
(n+225) • (n-24)
Which is the desired factorization
Final result :
(n + 225) • (n - 24)
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