Polynomial Zeros and Their Multiplicities

The video tutorial explains how to find the zeros of polynomials and their multiplicities. It begins with a basic introduction to zeros and multiplicities, followed by a detailed explanation of factoring quadratic forms to find zeros. The tutorial also covers the concept of difference of squares and how it can be used to determine zeros and their multiplicities. Throughout the video, various examples are provided to illustrate these concepts.

What is the first step in finding the zeros of a polynomial?

• Set the polynomial equal to zero

• Multiply all terms

• Divide by the highest degree term

• Add all coefficients

How can you express the polynomial x + 3 * x + 3 * x + 3 * x - 2 * x * X?

• (x + 3)^3 * (x - 2)

• (x + 3)^2 * (x - 2) * x

• (x + 3)^2 * (x - 2) * x^2

• (x + 3)^3 * (x - 2) * x^2

What is the multiplicity of the zero -3 in the given polynomial?

• 1

• 3

• 4

• 2

What is the multiplicity of the zero 2 in the polynomial?

• 1

• 2

• 3

• 4

What form is the equation x^4 - 19x^2 + 48 in?

• Quartic

• Cubic

• Quadratic

• Linear

Which pair of numbers are factors of 48 that add up to 19?

• 10 and 9

• 8 and 6

• 16 and 3

• 12 and 7

What is the result of factoring x^2 - 16?

• (x + 4)(x - 4)

• (x + 8)(x - 2)

• (x + 2)(x - 8)

• (x + 5)(x - 3)

What is the zero of the polynomial x^2 - 3x + 2?

• 3 and 4

• 2 and 3

• 1 and 2

• 4 and 5

What is the multiplicity of the zero -5 in the polynomial (x + 5)^4?

• 1

• 2

• 3

• 4

What is the multiplicity of the zero 5 in the polynomial (x - 5)^4?

• 4

• 3

• 2

• 1