Polynomial Zeros and Theorems

The video tutorial explains how to find all zeros of a polynomial, specifically X cubed plus X squared minus 10X plus 8. It begins by listing possible rational zeros using factors of the constant and leading coefficient. The remainder theorem is applied to identify factors, followed by synthetic division to simplify the polynomial. Finally, the quadratic is factored to find all zeros, resulting in X equals 1, -4, and 2.

What is the first step in finding the zeros of the polynomial X^3 + X^2 - 10X + 8?

• Listing possible rational zeros

• Using the Remainder Theorem

• Using the quadratic formula

• Graphing the polynomial

Which of the following is NOT a possible rational zero for the polynomial X^3 + X^2 - 10X + 8?

• 1

• 3

• 8

• 2

What theorem is used to determine if a number is a zero of the polynomial?

• Fundamental Theorem of Algebra

• Intermediate Value Theorem

• Remainder Theorem

• Factor Theorem

What is the result when 1 is substituted into the polynomial X^3 + X^2 - 10X + 8?

• -1

• 0

• 8

• 1

What method is used to divide the polynomial X^3 + X^2 - 10X + 8 by X - 1?

• Polynomial Remainder Theorem

• Partial Fraction Decomposition

• Synthetic Division

• Long Division

What is the remainder when the polynomial X^3 + X^2 - 10X + 8 is divided by X - 1?

• 1

• 0

• -1

• 8

What is the factored form of the polynomial X^3 + X^2 - 10X + 8 after using synthetic division?

• (X + 1)(X^2 + 2X - 8)

• (X - 1)(X^2 - 2X + 8)

• (X + 1)(X^2 - 2X + 8)

• (X - 1)(X^2 + 2X - 8)

Which pair of numbers multiply to -8 and add up to 2?

• 4 and -2

• -4 and 2

• 2 and -4

• -2 and 4

What is one of the zeros of the polynomial X^3 + X^2 - 10X + 8?

• 1

• 2

• -2

• 0

What are the zeros of the polynomial X^3 + X^2 - 10X + 8?

• 1, -4, 2

• 1, 4, -2

• -1, 4, 2

• 1, -4, -2