Module 4 - Polynomials Review

What is the degree of the polynomial?

y = 3x² - 7x⁴ + 9 - x⁴

^{Hint: Remember to look at the exponents of all the terms!}

• constant

• linear

• cubic

• quartic

How many terms in this polynomial?

y = 3x² - 7x⁴ + 9 - x⁴

^{Hint: Make sure all terms have been combined!}

• one - monomial

• two - binomial

• three - trinomial

• Polynomial

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)

What are the solutions for the polynomial

x³ + 4x² = 12x

Hint: Make sure equation is set up correctly before you factor!

• x = 1, x = 4, and x = 12

• x = 0, x = 1, and x = 4

• x = 0 and x = 2

• x = 0, x = 2 and x = -6

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

Tags

CCSS.HSF-IF.C.7C

Using your graphing calculator find the relative minimum of the polynomial
y = x⁴ - 5x³ + 5x² - 3

• (0, -3) and (3, -12)
• (2.91, -3) and (2.88, -12.71)
• (0, -3) and (2.88, -12.71)
• (-3, 0) and (-12.71, 2.88)

Using your calculator what is the relative maximum of the polynomial
y = x⁴ - 4x -1

• (1, -4)
• too many to find!
• none
• (-4, 1)

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)?

• $3x^3-3x^2+8x-9$
  

• $3x^2-3x+8-\frac{9}{x+1}$

• $3x^2+3x+8+\frac{7}{x+1}$
  

• $3x^3+3x+8+\frac{7}{x+1}$