Remainder and Factor Theorems

The video tutorial covers the factor and remainder theorems, starting with a quadratic example. It explains how to factorize a quadratic equation and verify its factors using the factor theorem. The remainder theorem is then introduced, showing how to find remainders when dividing polynomials. The tutorial includes examples and practice questions to reinforce understanding.

What is the main focus of the video tutorial?

• Geometry concepts

• Basics of algebra

• Factor and Remainder Theorems

• Introduction to calculus

What is the quadratic equation used in the example?

• x^2 - 3x - 10

• x^2 + 3x + 10

• x^2 + 5x - 6

• x^2 - 5x + 6

What are the factors of the quadratic x^2 - 3x - 10?

• x - 3 and x + 3

• x - 5 and x + 2

• x + 5 and x - 2

• x + 3 and x - 3

According to the Factor Theorem, if x - 5 is a factor, what should F(5) equal?

• 0

• -5

• 10

• 5

What is the result of substituting 5 into the quadratic equation x^2 - 3x - 10?

• -5

• 0

• 10

• 5

What is the main purpose of the Factor Theorem?

• To solve quadratic equations

• To find the roots of a polynomial

• To determine if a linear factor divides a polynomial

• To calculate the derivative of a function

What does the Remainder Theorem state about dividing by x - 2?

• It gives a remainder of 2

• It gives a remainder of 12

• It gives a remainder of -12

• It gives a remainder of 0

What is the remainder when x^2 - 3x - 10 is divided by x - 2?

• 0

• 2

• -12

• 12

What is the main purpose of the Remainder Theorem?

• To find the roots of a polynomial

• To solve quadratic equations

• To determine the remainder when a polynomial is divided by a linear factor

• To calculate the derivative of a function

What should F(-1) equal to show that x + 1 is a factor of X^3 + 4x^2 - 2x - 5?

• 0

• 5

• -1

• 1