Multiplicity and Graphing Polynomials in Factored Form

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

Which of the following could be the equation of the graph in factored form?

• y=-(x+1)(x-2)(x-4)

• y=(x+1)²(x-2)
  (x-4)³

• y = x(x+1)(x-2)
  (x-4)

• y=(x+1)³(x-3)
  (x-1)²

Which of the following could be the factored form for the equation representing the graph shown?

• (x+3)(x-2)(x-5)

• (x-5)²(x-2)(x+3)

• (x-3)(x+2)(x+5)²

• none of these

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

Which of the following could be the equation of this graph in factored form? (Be careful and pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x+4)(x+1)(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

What is the Factored Form for this graph? (Hint: does it have a multiplicity?)

• y= - (x+1)(x-2)(x-4)

• y= (x+1)²(x-3)(x-1)³

• y = 3x³ – 2x + 1

• y= (x+1)³(x-3)(x-1)²

• 2
• 1
• 4
• cannot be determined

Which is true about the equation of the graph shown?

• The function has an Odd degree

• The function has an Even degree

• The function has 5 real zeros

• The function has a positive leading coefficient

• a
• b
• c
• d