Unit 2 Lessons 12-20 Flashcard

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

Front

How do you perform polynomial long division?

Back

To perform polynomial long division, arrange the polynomials in descending order, divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract from the dividend, and repeat the process with the new polynomial.

Front

What is the result of dividing (2x^3 + 7x^2 - 6x - 8) by (x + 4)?

Back

The result is 2x^2 - x - 2.

Front

What is the result of dividing (2x^3 + 5x^2 + 9) by (x + 3)?

Back

The result is 2x^2 - x + 3.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

To determine the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator: if the degree of the numerator is less, the asymptote is y=0; if they are equal, the asymptote is y=(leading coefficient of numerator)/(leading coefficient of denominator); if the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the horizontal asymptote of the function with a leading coefficient of 4 in the numerator and a leading coefficient of 1 in the denominator?

Back

The horizontal asymptote is y=4.

Front

What is the horizontal asymptote of the function with a leading coefficient of 1 in the numerator and a leading coefficient of 2 in the denominator?

Back

The horizontal asymptote is y=1/2.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for x.