Zeros of Polynomials

Open Ended

Question of the Day:

What's your go-to karaoke song? Or what song would you sing (even just a chorus or verse) if asked?

Multiple Choice

The degree of a polynomial determines...

• the maximum number of x-intercepts

• the number of turning points

• if the end behavior is up or down

• the y-intercept

Multiple Choice

How many zeros does the polynomial function $$f\left(x\right)=3x^4+4x^{2\ }+8$$  have?

• 2

• 3

• 4

• 6

Multiple Choice

What are the zeros of the function?

• 4, 1

• -3, -1, 2, 5

• -3, -1, 30, 2, 5

• 3, 1, -2, -5

Multiple Choice

Which best describes the multiplicity of a root?

• It is the number of times the corresponding factor is repeated

• It is the highest degree of the polynomial

• It is the number of times x is multiplied by itself

• It is the number of x-intercepts on a graph

Multiple Choice

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

• {0 mult. 3, 5, 2}

• {−2 mult. 3, 3, 1}

• {0 mult. 3, 3, 2}

• {2 mult. 3, 3, 3}

Multiple Choice

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

• {0 mult. 3}

• {0, 3, 1}

• {0, −2, −1}

• {−2, 3, 1}

Poll

Brain Break! Breakfast Pastries!

• Bagel

• Muffin

• Donut/Very Sweet Pastry

• Danish/Croissant

• Other/I don't like breakfast p

Multiple Choice

Solve and find your x-intercepts:
0=x(x - 6)

• x=0 and x=-6
• x=1 and x=-6
• x=0 and x=6
• x=6

Multiple Choice

Find the zeros.

(x-5)(x+6)=0

• {5,5 }

• { -5,-5 }

• { -5,-6 }

• {5,-6 }

Multiple Choice

Find the zeros.

(x + 2)(x - 3) = 0

• { 2, 3 }

• { -2, -3 }

• { 2, 3 }

• { -2, 3 }

Multiple Choice

Find the zeros.

5(x+12)(x-12) = 0

• {5,12,-12}

• {-12, 12}

• {0,12,-12}

• {12}

Multiple Choice

Find the zeros.

(2x - 1)(x + 4) = 0

• { 1/2, -4 }

• { 1/2, 4 }

• { 2, -4 }

• { -2, 4 }

Multiple Choice

Find the zeros.

8x(2x + 4)(x - 6)

• x = - 2, 6, - 8

• x = 2, 6, 0

• x = - 2, 6, 0

• x = - 8, 4, 6

Multiple Choice

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

• x = -4, x = 3, x = -2
• x = -4, x = 3, x = 2 
• x = -4, x = -3, x = 2
• x = 4, x = 3, x = 2

Multiple Choice

Find the values of the zeros of the function y=(x+2)(x-3)(3x-5)

• x=-2, x=3, x=5/3

• x=2, x=-3, x= -5/3

• x=-2, x=3, x=3/5

• x=2, x=-3, x=-3/5

Multiple Choice

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

• x = 5, (2/3), 6, (7/4)
• x= -5, (3/2), (-4/7), 6
• x= 5, (-3/2), (4/7), -6
• x= 6, 5, -2/3, -4/7

Poll

Brain Break Pt. 2:

Pick a topic

(we're not discussing/debating them)

• The Met Gala

• Celebrity Beef

• NBA Finals

• Politics

• None/Other

Multiple Choice

What are the roots of the polynomial function?
y = 9(x + 2)(x - 7)³

• -2, 7 multiplicity 3
• -2, 7, 0
• 9, 2, -7 multiplicity 3
• 2, -7, 3

Multiple Choice

State the zeros of the polynomial (include multiplicity):
f(x) = x⁴(x+3)²(x - 2)

•  0, 3, 2
•  0(multiplicity of 4), -3 (multiplicity of 2), 2
• -3 (multiplicity of 2), 2
• 0, 2 (multiplicity of 3)

Multiple Choice

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

​What is a possible factored form of this polynomial given the zeros:

Multiple Choice

Write the factored form of the polynomial with roots x=-2. x=5, x=2/3

• y=(x-2)(x+5)(3x+2)

• y=(x-2)(x+5)(2x+3)

• y=(x+2)(x-5)(2x-3)

• y=(x+2)(x-5)(3x-2)

Multiple Choice

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

• (x + 5)³(x - 9)²(x + 2)(x - 4)
• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷
• (x + 5)³(x - 9)²(x + 2)
• (x + 5)(x - 9)(x + 2)(x - 4)

Multiple Choice

Which of the following is the correct equation for the function graphed?

• $$f\left(x\right)=\left(x-1\right)^{2\ }\left(x+2\right)^{2\ }$$  

• $$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^{2\ }$$  

• $$f\left(x\right)=\left(x-1\right)\left(x+2\right)$$  

• $$f\left(x\right)=\left(x+1\right)\left(x-2\right)$$  

Multiple Choice

What is the equation in factored form of the function graphed?

• $$f\left(x\right)=-\left(x+4\right)\left(x+1\right)^2\left(x-2\right)\left(x-4\right)$$  

• $$f\left(x\right)=-\left(x-4\right)\left(x-1\right)^2\left(x+2\right)\left(x+4\right)$$  

• $$f\left(x\right)=\left(x+4\right)\left(x+1\right)^{2\ }\left(x-2\right)\left(x-4\right)$$  

• $$f\left(x\right)=\left(x-4\right)\left(x-1\right)^{2\ }\left(x=2\right)\left(x+4\right)$$