# Algebra Examples

Find the Roots (Zeros)
Replace with .
To find the roots of the equation, replace with and solve.
Rewrite the equation as .
Factor the left side of the equation.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Simplify each term.
Raise to the power of .
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Add and .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Factor using the perfect square rule.
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Combine like factors.
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
The solution is the result of .
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