# Find the Symmetry (x^2-x-12)/(x-7)

Write the polynomial as an equation.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
There are three types of symmetry:
1. X-Axis Symmetry
2. Y-Axis Symmetry
3. Origin Symmetry
If exists on the graph, then the graph is symmetric about the:
1. X-Axis if exists on the graph
2. Y-Axis if exists on the graph
3. Origin if exists on the graph
Check if the graph is symmetric about the x-axis by plugging in for .
Remove parentheses.
Since the equation is not identical to the original equation, it is not symmetric to the x-axis.
Not symmetric to the x-axis
Check if the graph is symmetric about the y-axis by plugging in for .
Simplify .
Remove parentheses.
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Multiply by .
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
Since the equation is not identical to the original equation, it is not symmetric to the y-axis.
Not symmetric to the y-axis
Check if the graph is symmetric about the origin by plugging in for and for .
Solve for .
Simplify .
Remove parentheses.
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Multiply by .
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
Remove parentheses.
Simplify .
Remove parentheses.
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Multiply by .
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
Simplify .
Remove parentheses.
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Multiply by .
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Multiply by .
Multiply by .
Since the equation is not identical to the original equation, it is not symmetric to the origin.
Not symmetric to the origin
Determine the symmetry.
Not symmetric to the x-axis
Not symmetric to the y-axis
Not symmetric to the origin
Find the Symmetry (x^2-x-12)/(x-7)