Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•5x2) - 46x) + 24
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20x2 - 46x + 24 = 2 • (10x2 - 23x + 12)
Trying to factor by splitting the middle term
3.2 Factoring 10x2 - 23x + 12
The first term is, 10x2 its coefficient is 10 .
The middle term is, -23x its coefficient is -23 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 10 • 12 = 120
Step-2 : Find two factors of 120 whose sum equals the coefficient of the middle term, which is -23 .
| -120 | + | -1 | = | -121 | ||
| -60 | + | -2 | = | -62 | ||
| -40 | + | -3 | = | -43 | ||
| -30 | + | -4 | = | -34 | ||
| -24 | + | -5 | = | -29 | ||
| -20 | + | -6 | = | -26 | ||
| -15 | + | -8 | = | -23 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -8
10x2 - 15x - 8x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (2x-3)
Add up the last 2 terms, pulling out common factors :
4 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(5x-4) • (2x-3)
Which is the desired factorization
Final result :
2 • (2x - 3) • (5x - 4)
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