# Trigonometry Examples

Step 1
Factor .
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.
Raise to the power of .
Raise to the power of .
Multiply by .
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 .
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
 - + + -
Divide the highest order term in the dividend by the highest order term in divisor .
 - + + -
Multiply the new quotient term by the divisor.
 - + + - + -
The expression needs to be subtracted from the dividend, so change all the signs in
 - + + - - +
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 - + + - - + +
Pull the next terms from the original dividend down into the current dividend.
 - + + - - + + +
Divide the highest order term in the dividend by the highest order term in divisor .
 + - + + - - + + +
Multiply the new quotient term by the divisor.
 + - + + - - + + + + -
The expression needs to be subtracted from the dividend, so change all the signs in
 + - + + - - + + + - +
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + - + + - - + + + - + +
Pull the next terms from the original dividend down into the current dividend.
 + - + + - - + + + - + + -
Divide the highest order term in the dividend by the highest order term in divisor .
 + + - + + - - + + + - + + -
Multiply the new quotient term by the divisor.
 + + - + + - - + + + - + + - + -
The expression needs to be subtracted from the dividend, so change all the signs in
 + + - + + - - + + + - + + - - +
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + + - + + - - + + + - + + - - +
Since the remander is , the final answer is the quotient.
Write as a set of factors.
Factor using the AC method.
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.
Remove unnecessary parentheses.
Step 2
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.
Step 3
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Step 4
Cancel the common factor of .
Cancel the common factor.
Divide by .
Step 5
To find the holes in the graph, look at the denominator factors that were cancelled.
Step 6
To find the coordinates of the holes, set each factor that was cancelled equal to , solve, and substitute back in to .
Set equal to .
Subtract from both sides of the equation.
Substitute for in and simplify.
Substitute for to find the coordinate of the hole.
Subtract from .
Set equal to .
Subtract from both sides of the equation.
Substitute for in and simplify.
Substitute for to find the coordinate of the hole.
Subtract from .
The holes in the graph are the points where any of the cancelled factors are equal to .
Step 7