Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•32x2) + 96x) + 48
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
36x2 + 96x + 48 = 12 • (3x2 + 8x + 4)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 8x + 4
The first term is, 3x2 its coefficient is 3 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 3 • 4 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is 8 .
| -12 | + | -1 | = | -13 | ||
| -6 | + | -2 | = | -8 | ||
| -4 | + | -3 | = | -7 | ||
| -3 | + | -4 | = | -7 | ||
| -2 | + | -6 | = | -8 | ||
| -1 | + | -12 | = | -13 | ||
| 1 | + | 12 | = | 13 | ||
| 2 | + | 6 | = | 8 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 6
3x2 + 2x + 6x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+2)
Add up the last 2 terms, pulling out common factors :
2 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(x+2) • (3x+2)
Which is the desired factorization
Final result :
12 • (3x + 2) • (x + 2)
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