Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-200x-240000
The first term is, x2 its coefficient is 1 .
The middle term is, -200x its coefficient is -200 .
The last term, "the constant", is -240000
Step-1 : Multiply the coefficient of the first term by the constant 1 • -240000 = -240000
Step-2 : Find two factors of -240000 whose sum equals the coefficient of the middle term, which is -200 .
| -240000 | + | 1 | = | -239999 | ||
| -120000 | + | 2 | = | -119998 | ||
| -80000 | + | 3 | = | -79997 | ||
| -60000 | + | 4 | = | -59996 | ||
| -48000 | + | 5 | = | -47995 | ||
| -40000 | + | 6 | = | -39994 | ||
| -30000 | + | 8 | = | -29992 | ||
| -24000 | + | 10 | = | -23990 | ||
| -20000 | + | 12 | = | -19988 | ||
| -16000 | + | 15 | = | -15985 | ||
| -15000 | + | 16 | = | -14984 | ||
| -12000 | + | 20 | = | -11980 | ||
| -10000 | + | 24 | = | -9976 | ||
| -9600 | + | 25 | = | -9575 | ||
| -8000 | + | 30 | = | -7970 | ||
| -7500 | + | 32 | = | -7468 | ||
| -6000 | + | 40 | = | -5960 | ||
| -5000 | + | 48 | = | -4952 | ||
| -4800 | + | 50 | = | -4750 | ||
| -4000 | + | 60 | = | -3940 | ||
| -3750 | + | 64 | = | -3686 | ||
| -3200 | + | 75 | = | -3125 | ||
| -3000 | + | 80 | = | -2920 | ||
| -2500 | + | 96 | = | -2404 | ||
| -2400 | + | 100 | = | -2300 | ||
| -2000 | + | 120 | = | -1880 | ||
| -1920 | + | 125 | = | -1795 | ||
| -1875 | + | 128 | = | -1747 | ||
| -1600 | + | 150 | = | -1450 | ||
| -1500 | + | 160 | = | -1340 | ||
| -1250 | + | 192 | = | -1058 | ||
| -1200 | + | 200 | = | -1000 | ||
| -1000 | + | 240 | = | -760 | ||
| -960 | + | 250 | = | -710 | ||
| -800 | + | 300 | = | -500 | ||
| -750 | + | 320 | = | -430 | ||
| -640 | + | 375 | = | -265 | ||
| -625 | + | 384 | = | -241 | ||
| -600 | + | 400 | = | -200 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -600 and 400
x2 - 600x + 400x - 240000
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-600)
Add up the last 2 terms, pulling out common factors :
400 • (x-600)
Step-5 : Add up the four terms of step 4 :
(x+400) • (x-600)
Which is the desired factorization
Final result :
(x + 400) • (x - 600)
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