Precalculus Examples

Find the Roots (Zeros) f(x)=2x^3-x^2-18x+9
Step 1
Set equal to .
Step 2
Solve for .
Tap for more steps...
Step 2.1
Factor the left side of the equation.
Tap for more steps...
Step 2.1.1
Factor out the greatest common factor from each group.
Tap for more steps...
Step 2.1.1.1
Group the first two terms and the last two terms.
Step 2.1.1.2
Factor out the greatest common factor (GCF) from each group.
Step 2.1.2
Factor the polynomial by factoring out the greatest common factor, .
Step 2.1.3
Rewrite as .
Step 2.1.4
Factor.
Tap for more steps...
Step 2.1.4.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.1.4.2
Remove unnecessary parentheses.
Step 2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3
Set equal to and solve for .
Tap for more steps...
Step 2.3.1
Set equal to .
Step 2.3.2
Solve for .
Tap for more steps...
Step 2.3.2.1
Add to both sides of the equation.
Step 2.3.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.3.2.2.1
Divide each term in by .
Step 2.3.2.2.2
Simplify the left side.
Tap for more steps...
Step 2.3.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.3.2.2.2.1.1
Cancel the common factor.
Step 2.3.2.2.2.1.2
Divide by .
Step 2.4
Set equal to and solve for .
Tap for more steps...
Step 2.4.1
Set equal to .
Step 2.4.2
Subtract from both sides of the equation.
Step 2.5
Set equal to and solve for .
Tap for more steps...
Step 2.5.1
Set equal to .
Step 2.5.2
Add to both sides of the equation.
Step 2.6
The final solution is all the values that make true.
Step 3