Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+5x-1800
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is -1800
Step-1 : Multiply the coefficient of the first term by the constant 1 • -1800 = -1800
Step-2 : Find two factors of -1800 whose sum equals the coefficient of the middle term, which is 5 .
| -1800 | + | 1 | = | -1799 | ||
| -900 | + | 2 | = | -898 | ||
| -600 | + | 3 | = | -597 | ||
| -450 | + | 4 | = | -446 | ||
| -360 | + | 5 | = | -355 | ||
| -300 | + | 6 | = | -294 | ||
| -225 | + | 8 | = | -217 | ||
| -200 | + | 9 | = | -191 | ||
| -180 | + | 10 | = | -170 | ||
| -150 | + | 12 | = | -138 | ||
| -120 | + | 15 | = | -105 | ||
| -100 | + | 18 | = | -82 | ||
| -90 | + | 20 | = | -70 | ||
| -75 | + | 24 | = | -51 | ||
| -72 | + | 25 | = | -47 | ||
| -60 | + | 30 | = | -30 | ||
| -50 | + | 36 | = | -14 | ||
| -45 | + | 40 | = | -5 | ||
| -40 | + | 45 | = | 5 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -40 and 45
x2 - 40x + 45x - 1800
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-40)
Add up the last 2 terms, pulling out common factors :
45 • (x-40)
Step-5 : Add up the four terms of step 4 :
(x+45) • (x-40)
Which is the desired factorization
Final result :
(x + 45) • (x - 40)
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