2.11.21 Zeros, Linear Factors, Multiplicity & Dividing Poly

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

How does a multiplicity of 2 affect the graph?

• cross

• bounce

• wiggle (change direction)

Tags

CCSS.HSF.BF.B.3

How does a multiplicity of 1 affect the graph?

• bounce

• cross

• wiggle (change direction)

Tags

CCSS.HSA.APR.B.3

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

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

• $f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

• $f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

• $f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

• $f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

Tags

CCSS.HSA.APR.B.3

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

 $\frac{2x^3-5x^2+3x+7}{x-2}$  

•  $2x^3-x^2+x+9$  
  

•  $2x^2-x+1$  
  

•  $2x^2-x+1+\frac{9}{x-2}$  
  

•  $2x^2-9x-15-\frac{23}{x-2}$  
  

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1
• 6   -4   3   1   0
• 6   -4   0   3   1
• -6   4   0   -3   -1

Tags

CCSS.HSA.APR.D.6

 $\frac{2x^3-5x^2-4x-25}{x-4}$  

•  $2x^2+3x+8-\frac{57}{x-4}$  

•  $2x^2-13x-56$  

•  $2x^2+3x+8+\frac{7}{x-4}$  

•  $2x^2-3x-16-\frac{89}{x-4}$  

Tags

CCSS.HSA.APR.D.6