Examples

Find the Equation Given the Roots
,
Step 1
Roots are the points where the graph intercepts with the x-axis .
at the roots
Step 2
The root at was found by solving for when and .
The factor is
Step 3
The root at was found by solving for when and .
The factor is
Step 4
Combine all the factors into a single equation.
Step 5
Multiply all the factors to simplify the equation .
Tap for more steps...
Step 5.1
Expand using the FOIL Method.
Tap for more steps...
Step 5.1.1
Apply the distributive property.
Step 5.1.2
Apply the distributive property.
Step 5.1.3
Apply the distributive property.
Step 5.2
Simplify and combine like terms.
Tap for more steps...
Step 5.2.1
Simplify each term.
Tap for more steps...
Step 5.2.1.1
Multiply by .
Step 5.2.1.2
Move to the left of .
Step 5.2.1.3
Combine and .
Step 5.2.1.4
Multiply .
Tap for more steps...
Step 5.2.1.4.1
Multiply by .
Step 5.2.1.4.2
Combine and .
Step 5.2.2
To write as a fraction with a common denominator, multiply by .
Step 5.2.3
Combine and .
Step 5.2.4
Combine the numerators over the common denominator.
Step 5.2.5
To write as a fraction with a common denominator, multiply by .
Step 5.2.6
Combine and .
Step 5.2.7
Combine the numerators over the common denominator.
Step 5.2.8
Combine the numerators over the common denominator.
Step 5.3
Simplify the numerator.
Tap for more steps...
Step 5.3.1
Move to the left of .
Step 5.3.2
Multiply by .
Step 5.3.3
Subtract from .
Step 5.3.4
Factor by grouping.
Tap for more steps...
Step 5.3.4.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Step 5.3.4.1.1
Factor out of .
Step 5.3.4.1.2
Rewrite as plus
Step 5.3.4.1.3
Apply the distributive property.
Step 5.3.4.2
Factor out the greatest common factor from each group.
Tap for more steps...
Step 5.3.4.2.1
Group the first two terms and the last two terms.
Step 5.3.4.2.2
Factor out the greatest common factor (GCF) from each group.
Step 5.3.4.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5.4
Expand using the FOIL Method.
Tap for more steps...
Step 5.4.1
Apply the distributive property.
Step 5.4.2
Apply the distributive property.
Step 5.4.3
Apply the distributive property.
Step 5.5
Simplify and combine like terms.
Tap for more steps...
Step 5.5.1
Simplify each term.
Tap for more steps...
Step 5.5.1.1
Multiply by by adding the exponents.
Tap for more steps...
Step 5.5.1.1.1
Move .
Step 5.5.1.1.2
Multiply by .
Step 5.5.1.2
Multiply by .
Step 5.5.1.3
Rewrite as .
Step 5.5.1.4
Multiply by .
Step 5.5.2
Subtract from .
Step 5.6
Split the fraction into two fractions.
Step 5.7
Split the fraction into two fractions.
Step 5.8
Cancel the common factor of .
Tap for more steps...
Step 5.8.1
Cancel the common factor.
Step 5.8.2
Divide by .
Step 5.9
Move the negative in front of the fraction.
Step 6
Enter YOUR Problem
Mathway requires javascript and a modern browser.