# Precalculus Examples

Find the Equation with Real Coefficients
, ,
Step 1
Since the roots of an equation are the points where the solution is , set each root as a factor of the equation that equals .
Step 2
Simplify.
Step 2.1
Expand using the FOIL Method.
Step 2.1.1
Apply the distributive property.
Step 2.1.2
Apply the distributive property.
Step 2.1.3
Apply the distributive property.
Step 2.2
Simplify terms.
Step 2.2.1
Combine the opposite terms in .
Step 2.2.1.1
Reorder the factors in the terms and .
Step 2.2.1.2
Subtract from .
Step 2.2.1.3
Step 2.2.2
Simplify each term.
Step 2.2.2.1
Multiply by .
Step 2.2.2.2
Multiply by .
Step 2.3
Expand using the FOIL Method.
Step 2.3.1
Apply the distributive property.
Step 2.3.2
Apply the distributive property.
Step 2.3.3
Apply the distributive property.
Step 2.4
Simplify each term.
Step 2.4.1
Multiply by by adding the exponents.
Step 2.4.1.1
Multiply by .
Step 2.4.1.1.1
Raise to the power of .
Step 2.4.1.1.2
Use the power rule to combine exponents.
Step 2.4.1.2