Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - 22x2) - 28x) - 48
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-4x2 - 28x - 48 = -4 • (x2 + 7x + 12)
Trying to factor by splitting the middle term
3.2 Factoring x2 + 7x + 12
The first term is, x2 its coefficient is 1 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 1 • 12 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is 7 .
| -12 | + | -1 | = | -13 | ||
| -6 | + | -2 | = | -8 | ||
| -4 | + | -3 | = | -7 | ||
| -3 | + | -4 | = | -7 | ||
| -2 | + | -6 | = | -8 | ||
| -1 | + | -12 | = | -13 | ||
| 1 | + | 12 | = | 13 | ||
| 2 | + | 6 | = | 8 | ||
| 3 | + | 4 | = | 7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 4
x2 + 3x + 4x + 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
4 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+3)
Which is the desired factorization
Final result :
-4 • (x + 4) • (x + 3)
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