Understanding Factors of Polynomials

This video tutorial explores how to determine if a given binomial is a factor of a polynomial using graphical analysis. It revisits the remainder theorem and applies it to four examples, using a TI-84 graphing calculator to verify factors and calculate remainders. The video covers the process of identifying factors by checking x-intercepts and calculating function values at specific points.

What theorem is used to determine if a binomial is a factor of a polynomial?

• Graphical Theorem

• Factor Theorem

• Remainder Theorem

• Polynomial Theorem

In the first example, what value of c is used to check if x + 2 is a factor?

• -2

• 0

• 2

• 1

What is the x-intercept of the polynomial if x + 2 is a factor?

• (-2, 0)

• (0, 2)

• (2, 0)

• (0, -2)

What is the remainder when the polynomial is divided by x - 1?

• 0

• 10

• 20

• 1

In the second example, what is the value of c for the binomial x - 1?

• 1

• 0

• -1

• 2

What is the function value at x = 0 for the quadratic function in Example 3?

• 2

• 1

• -1

• 0

In Example 3, what is the x-intercept if x is a factor?

• (0, 0)

• (1, 0)

• (2, 0)

• (-1, 0)

What is the value of c when transforming 2x - 3 into the form x - c?

• 0.5

• 2

• 1.5

• 3

What is the x-intercept of the polynomial if 2x - 3 is a factor?

• (3, 0)

• (0, 1.5)

• (0, 3)

• (1.5, 0)

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

• 0

• 1

• 1.5

• 3