Polynomials and Quadratics Review

Write a polynomial in factor form with zeros at

x = 1, x = -1 x = 0

Hint: How do you write factors from zeros?

• (x - 1)(x + 1)

• x(x - 1)(x + 1)

• x²(x - 1)(x + 1)

• x(x - 1)(x - 1)

Write a polynomial with the given zeros

x = 1, -1, 2

Hint: What are the factors for the given zeros?

• x³ - 2x² - x + 2

• x³ + 2x² + x - 2

• x³ - 2x² + x + 2

• x³ - 2x² - x - 2

What does multiplicity of a zero mean?

• Look at the number of terms
• How many times the zero repeats
• Find the sum of all the coefficients
• Ratio your x and y

What are the zeros of the polynomial and state their multiplicity at each.

y = (x - 5)(x + 2)²

^{Hint: Where do you look to find multiplicity?}

• x = 5 multi 1, x = 2 multi 2

• x = -5 multi 2, x = -2 multi 1

• x = 5 multi 1, x = -2 multi 2

• x = 5 multi 2, x = -2 multi 1

What is the quotient when (3x³ + 5x - 1) is divided by (x + 1)?

Given the polynomial 4x² -33x -27.

Is k = 9 a zero of the function?

• Yes, the remainder is 0

• No, the remainder is 0

• Yes, the remainder is 12

• No, the remainder is 12

What is the quotient when x² - 6x + 8 is divided by (x - 2) ?

• x - 6

• x - 9 + 2/(x - 2)

• x - 4

• x - 8 + 3/(x - 2)

Which term is missing in this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

Hint: You are using synthetic division.

• x⁴

• x³

• x²

• x

What is the proper way to write the quotient for the following problem?

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x - 2) using synthetic division. His work is shown above.

Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.