Write the polynomial as an equation.

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 .

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 .

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)