Algebra Examples

Solve by Factoring x^3-3x^2+4x-12=0
Step 1
Factor out the greatest common factor from each group.
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Step 1.1
Group the first two terms and the last two terms.
Step 1.2
Factor out the greatest common factor (GCF) from each group.
Step 2
Factor the polynomial by factoring out the greatest common factor, .
Step 3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Add to both sides of the equation.
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Solve for .
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.2.3
Simplify .
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Step 5.2.3.1
Rewrite as .
Step 5.2.3.2
Rewrite as .
Step 5.2.3.3
Rewrite as .
Step 5.2.3.4
Rewrite as .
Step 5.2.3.5
Pull terms out from under the radical, assuming positive real numbers.
Step 5.2.3.6
Move to the left of .
Step 5.2.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.2.4.1
First, use the positive value of the to find the first solution.
Step 5.2.4.2
Next, use the negative value of the to find the second solution.
Step 5.2.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6
The final solution is all the values that make true.