Set each factor equal to zero and solve for x.

Identify the leading term (term with the highest degree). Consider the sign and the exponent of the variable to determine the end behavior.

Divide the highest degree term of the dividend by the highest degree term of the divisor. Multiply the divisor by this term and subtract from the dividend. Repeat until the degree of the new dividend is less than the degree of the divisor.

Start with 1 at the top. Each number is the sum of the two numbers directly above it. The nth row gives the coefficients for (a+b)^(n-1).

Use the formula $(a + b)^n = \sum (n choose k) * a^(n-k) * b^k$, where $(n choose k)$ is the binomial coefficient.

Set the denominator equal to zero and solve for x. Exclude any values that also make the numerator zero (these are holes).

Compare the degrees of the numerator and denominator. If numerator degree < denominator degree, y=0. If numerator degree = denominator degree, y = ratio of leading coefficients. If numerator degree > denominator degree, there is no horizontal asymptote (may have a slant asymptote).

Set x = 0 and evaluate the function.

Set the numerator equal to zero and solve for x. Exclude any values that also make the denominator zero (these are vertical asymptotes or holes).

Factor both the numerator and the denominator. Cancel any common factors.

Polynomial expressed as a product of its factors.

Polynomial written in descending order of powers.

The x-intercepts of the function's graph.

Vertical lines where the function approaches infinity or negative infinity.

Points where a function is not defined, but the limit exists.

A method to divide one polynomial by another.

The result of dividing one polynomial by another, excluding the remainder.

The polynomial left over after polynomial long division, with a degree less than the divisor.

A method to expand expressions of the form $(a + b)^n$.

The coefficients in the expansion of $(a+b)^n$, often found using Pascal's Triangle.

$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$

$f(x) = g(x)q(x) + r(x)$ where $q(x)$ is the quotient and $r(x)$ is the remainder.

$f(x) = q(x) + \frac{r(x)}{g(x)}$, where $q(x)$ represents the slant asymptote if the degree of $g(x)$ is 1.

Numerator degree < denominator degree.

Numerator degree = denominator degree.

Numerator degree > denominator degree.

$\binom{n}{k} = \frac{n!}{k!(n-k)!}$