Remainder and Factor Theorems

This video tutorial covers the remainder and factor theorems, explaining how to determine the remainder when dividing polynomials and how to identify factors of polynomials. It includes examples using both the remainder theorem and synthetic division, as well as the factor theorem, to solve polynomial equations and verify factors.

What is one of the objectives of this lesson?

• To study calculus

• To understand the remainder theorem

• To explore trigonometric identities

• To learn about quadratic equations

According to the remainder theorem, what is the remainder when a polynomial P(x) is divided by x - r?

• Zero

• A constant equal to P(r)

• The divisor

• P(x) itself

In the example given, what is the remainder when 5x^2 - 2x + 1 is divided by x + 2 using the remainder theorem?

• 10

• 30

• 15

• 25

What is the first step in synthetic division?

• Multiply the divisor by the dividend

• Arrange the coefficients of the dividend in descending powers of x

• Add the coefficients

• Subtract the divisor from the dividend

What is the remainder when 2x^4 + 5x^3 + 2x^2 - 7x - 15 is divided by 2x - 3 using synthetic division?

• 6

• 5

• 7

• 8

What does the factor theorem state about a polynomial P(x) and a factor x - r?

• x - r is never a factor

• P(x) is a factor of x - r

• x - r is a factor if P(r) is zero

• P(x) is always zero

In the example, what is the value of k for which x + 4 is a factor of x^4 + kx^3 - 4x^2?

• 3

• 2

• 4

• 1