Understanding the Factor Theorem

This video tutorial covers the factor theorem, starting with quadratic equations and moving to cubic expressions. It explains how to find factors and solutions using factorization and polynomial long division. The video also demonstrates how to apply the factor theorem in exam questions and solve cubic equations. Advanced applications of the factor theorem are discussed, and the video concludes with additional resources for further practice.

What is the solution for the factor (x + 10) when set to zero?

• x = 0

• x = -10

• x = 2

• x = 10

What is the factor corresponding to the solution x = 2 for a quadratic equation?

• x + 10

• x - 10

• x - 2

• x + 2

If substituting x = 1 into a cubic expression results in zero, what is the factor?

• x - 2

• x - 1

• x + 1

• x + 2

If f(-4) does not result in zero, what can be concluded about x + 4?

• x - 4 is a factor

• x + 4 is a factor

• x - 4 is not a factor

• x + 4 is not a factor

How do you verify that x + 5 is a factor of a polynomial?

• Substitute x = 5 and check if the result is non-zero

• Substitute x = 5 and check if the result is zero

• Substitute x = -5 and check if the result is zero

• Substitute x = 0 and check if the result is zero

What is the first step in factorizing a cubic polynomial using the Factor Theorem?

• Find the derivative of the polynomial

• Set the polynomial equal to zero

• Substitute random numbers to find a factor

• Use polynomial long division

What is the result of dividing a cubic polynomial by a linear factor using polynomial long division?

• Another cubic polynomial

• A constant

• A quadratic polynomial

• A linear polynomial

What is the solution derived from the factor x - 3 in a cubic equation?

• x = 3

• x = -3

• x = 0

• x = 1

What is the correct factor for the expression 2x + 1 when using the Factor Theorem?

• x = -1

• x = 1/2

• x = 2

• x = -1/2

How do you determine the factor from a solution of x = -1/2 for the expression 2x + 1?

• 2x - 1

• x + 1/2

• 2x + 1

• x - 1/2