Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+32x+240
The first term is, x2 its coefficient is 1 .
The middle term is, +32x its coefficient is 32 .
The last term, "the constant", is +240
Step-1 : Multiply the coefficient of the first term by the constant 1 • 240 = 240
Step-2 : Find two factors of 240 whose sum equals the coefficient of the middle term, which is 32 .
| -240 | + | -1 | = | -241 | ||
| -120 | + | -2 | = | -122 | ||
| -80 | + | -3 | = | -83 | ||
| -60 | + | -4 | = | -64 | ||
| -48 | + | -5 | = | -53 | ||
| -40 | + | -6 | = | -46 | ||
| -30 | + | -8 | = | -38 | ||
| -24 | + | -10 | = | -34 | ||
| -20 | + | -12 | = | -32 | ||
| -16 | + | -15 | = | -31 | ||
| -15 | + | -16 | = | -31 | ||
| -12 | + | -20 | = | -32 | ||
| -10 | + | -24 | = | -34 | ||
| -8 | + | -30 | = | -38 | ||
| -6 | + | -40 | = | -46 | ||
| -5 | + | -48 | = | -53 | ||
| -4 | + | -60 | = | -64 | ||
| -3 | + | -80 | = | -83 | ||
| -2 | + | -120 | = | -122 | ||
| -1 | + | -240 | = | -241 | ||
| 1 | + | 240 | = | 241 | ||
| 2 | + | 120 | = | 122 | ||
| 3 | + | 80 | = | 83 | ||
| 4 | + | 60 | = | 64 | ||
| 5 | + | 48 | = | 53 | ||
| 6 | + | 40 | = | 46 | ||
| 8 | + | 30 | = | 38 | ||
| 10 | + | 24 | = | 34 | ||
| 12 | + | 20 | = | 32 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 12 and 20
x2 + 12x + 20x + 240
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+12)
Add up the last 2 terms, pulling out common factors :
20 • (x+12)
Step-5 : Add up the four terms of step 4 :
(x+20) • (x+12)
Which is the desired factorization
Final result :
(x + 20) • (x + 12)
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