Polynomial Functions and Their Properties

The video is a comprehensive review session for the Algebra 2 Regents Exam, covering key topics such as polynomial factoring, rational expressions, exponents, radicals, exponential and logarithmic functions, and general function analysis. The instructor provides detailed explanations and examples, emphasizing the importance of understanding concepts and solving problems algebraically. The session also includes tips for test-taking and encourages students to practice and review thoroughly.

What is the first step in factoring a polynomial completely?

• Identify the zeros of the polynomial

• Find the greatest common factor

• Graph the polynomial

• Solve the polynomial equation

How can you determine if a binomial is a factor of a polynomial?

• By solving the polynomial equation

• By finding the derivative of the polynomial

• By checking if the binomial divides the polynomial evenly

• By graphing the polynomial

What is the purpose of polynomial long division?

• To factor a polynomial completely

• To divide one polynomial by another and find the quotient and remainder

• To simplify a polynomial

• To find the zeros of a polynomial

In polynomial long division, what should you do if a term is missing in the dividend?

• Ignore the missing term

• Add a placeholder term with a coefficient of zero

• Multiply the dividend by the divisor

• Subtract the divisor from the dividend

What is the remainder when a polynomial P(x) is divided by a linear factor (x + 4) according to the remainder theorem?

• The remainder is the value of P(x) at x = 4.

• The remainder is the leading coefficient of P(x).

• The remainder is always zero.

• The remainder is the value of P(x) at x = -4.

When solving rational equations, what should you check for after finding the solutions?

• If any solution makes the denominator zero.

• If any solution is a negative number.

• If any solution makes the numerator zero.

• If any solution is greater than 10.

How can you express the sixth root of x using exponents?

• x^(-6)

• x^(6)

• x^6

• x^(1/6)

What is the growth rate when the growth factor is 1.061858?

• 7%

• 8%

• 6%

• 5%

Which of the following is the inverse of the function y = log base 3 of x?

• y = 1/3^x

• y = log base x of 3

• y = x^3

• y = 3^x

How does the graph of a polynomial with a positive leading coefficient and an even degree behave?

• It forms a straight line

• One end points up, the other down

• Both ends point downwards

• Both ends point upwards