Polynomials: Zeros, multiplicity, turning points, etc.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

Tags

CCSS.HSF-IF.C.7C

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

Tags

CCSS.HSF-IF.C.7C

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3
• 3, -3, 4, 1
• 4, 1, -3
• 3, -4, -1, 3

Tags

CCSS.HSF-IF.C.7C

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

• 0, 6, -5
• 6, -5
• 0, -6, 5
• 1, -6, 5

Tags

CCSS.HSF-IF.C.7C

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

• -2, 7 multiplicity 3
• -2, 7, 3
• 2, -7 multiplicity 3
• 2, -7, 3

Tags

CCSS.HSF-IF.C.7C

Which one of these are not a zero of  $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$  ?

• 0

• 1

• -5

• -1

Tags

CCSS.HSF-IF.C.7C

Which one of these are not a zero of  $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$  

• -2
  

• 0

•  $-\frac{1}{3}$  

• -7

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=1 for the function  $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$  ?

• 2

• 1

• 4

• 3

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

• 1

• 2

• 3

• 4

Tags

CCSS.HSF-IF.C.7C

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

• $f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

• $f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

• $f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

• $f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

Tags

CCSS.HSA.APR.B.3