Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+250x-750000
The first term is, x2 its coefficient is 1 .
The middle term is, +250x its coefficient is 250 .
The last term, "the constant", is -750000
Step-1 : Multiply the coefficient of the first term by the constant 1 • -750000 = -750000
Step-2 : Find two factors of -750000 whose sum equals the coefficient of the middle term, which is 250 .
| -750000 | + | 1 | = | -749999 | ||
| -375000 | + | 2 | = | -374998 | ||
| -250000 | + | 3 | = | -249997 | ||
| -187500 | + | 4 | = | -187496 | ||
| -150000 | + | 5 | = | -149995 | ||
| -125000 | + | 6 | = | -124994 | ||
| -93750 | + | 8 | = | -93742 | ||
| -75000 | + | 10 | = | -74990 | ||
| -62500 | + | 12 | = | -62488 | ||
| -50000 | + | 15 | = | -49985 | ||
| -46875 | + | 16 | = | -46859 | ||
| -37500 | + | 20 | = | -37480 | ||
| -31250 | + | 24 | = | -31226 | ||
| -30000 | + | 25 | = | -29975 | ||
| -25000 | + | 30 | = | -24970 | ||
| -18750 | + | 40 | = | -18710 | ||
| -15625 | + | 48 | = | -15577 | ||
| -15000 | + | 50 | = | -14950 | ||
| -12500 | + | 60 | = | -12440 | ||
| -10000 | + | 75 | = | -9925 | ||
| -9375 | + | 80 | = | -9295 | ||
| -7500 | + | 100 | = | -7400 | ||
| -6250 | + | 120 | = | -6130 | ||
| -6000 | + | 125 | = | -5875 | ||
| -5000 | + | 150 | = | -4850 | ||
| -3750 | + | 200 | = | -3550 | ||
| -3125 | + | 240 | = | -2885 | ||
| -3000 | + | 250 | = | -2750 | ||
| -2500 | + | 300 | = | -2200 | ||
| -2000 | + | 375 | = | -1625 | ||
| -1875 | + | 400 | = | -1475 | ||
| -1500 | + | 500 | = | -1000 | ||
| -1250 | + | 600 | = | -650 | ||
| -1200 | + | 625 | = | -575 | ||
| -1000 | + | 750 | = | -250 | ||
| -750 | + | 1000 | = | 250 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -750 and 1000
x2 - 750x + 1000x - 750000
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-750)
Add up the last 2 terms, pulling out common factors :
1000 • (x-750)
Step-5 : Add up the four terms of step 4 :
(x+1000) • (x-750)
Which is the desired factorization
Final result :
(x + 1000) • (x - 750)
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