Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•3•5x2) + 280x) + 45
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
60x2 + 280x + 45 = 5 • (12x2 + 56x + 9)
Trying to factor by splitting the middle term
3.2 Factoring 12x2 + 56x + 9
The first term is, 12x2 its coefficient is 12 .
The middle term is, +56x its coefficient is 56 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 12 • 9 = 108
Step-2 : Find two factors of 108 whose sum equals the coefficient of the middle term, which is 56 .
| -108 | + | -1 | = | -109 | ||
| -54 | + | -2 | = | -56 | ||
| -36 | + | -3 | = | -39 | ||
| -27 | + | -4 | = | -31 | ||
| -18 | + | -6 | = | -24 | ||
| -12 | + | -9 | = | -21 | ||
| -9 | + | -12 | = | -21 | ||
| -6 | + | -18 | = | -24 | ||
| -4 | + | -27 | = | -31 | ||
| -3 | + | -36 | = | -39 | ||
| -2 | + | -54 | = | -56 | ||
| -1 | + | -108 | = | -109 | ||
| 1 | + | 108 | = | 109 | ||
| 2 | + | 54 | = | 56 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 54
12x2 + 2x + 54x + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (6x+1)
Add up the last 2 terms, pulling out common factors :
9 • (6x+1)
Step-5 : Add up the four terms of step 4 :
(2x+9) • (6x+1)
Which is the desired factorization
Final result :
5 • (6x + 1) • (2x + 9)
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