Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0-(2•((3x2-x)+2)))+3x)-1
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2-x+2
The first term is, 3x2 its coefficient is 3 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 3 • 2 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -1 .
| -6 | + | -1 | = | -7 | ||
| -3 | + | -2 | = | -5 | ||
| -2 | + | -3 | = | -5 | ||
| -1 | + | -6 | = | -7 | ||
| 1 | + | 6 | = | 7 | ||
| 2 | + | 3 | = | 5 | ||
| 3 | + | 2 | = | 5 | ||
| 6 | + | 1 | = | 7 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 2 :
((0 - 2 • (3x2 - x + 2)) + 3x) - 1
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
-6x2 + 5x - 5 = -1 • (6x2 - 5x + 5)
Trying to factor by splitting the middle term
4.2 Factoring 6x2 - 5x + 5
The first term is, 6x2 its coefficient is 6 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 6 • 5 = 30
Step-2 : Find two factors of 30 whose sum equals the coefficient of the middle term, which is -5 .
| -30 | + | -1 | = | -31 | ||
| -15 | + | -2 | = | -17 | ||
| -10 | + | -3 | = | -13 | ||
| -6 | + | -5 | = | -11 | ||
| -5 | + | -6 | = | -11 | ||
| -3 | + | -10 | = | -13 | ||
| -2 | + | -15 | = | -17 | ||
| -1 | + | -30 | = | -31 | ||
| 1 | + | 30 | = | 31 | ||
| 2 | + | 15 | = | 17 | ||
| 3 | + | 10 | = | 13 | ||
| 5 | + | 6 | = | 11 | ||
| 6 | + | 5 | = | 11 | ||
| 10 | + | 3 | = | 13 | ||
| 15 | + | 2 | = | 17 | ||
| 30 | + | 1 | = | 31 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-6x2 + 5x - 5
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