Chapter 5 Polynomial Functions and Factors Quiz

Factor Completely:
3x⁴ + 3x³ - 12x² - 12x

• 3x(x³ + x²- 4x - 4)
• 3x(x²-4)(x+1)
• 3x(x+2)(x-2)(x+1)
• 3x(x²+4)(x-1)

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)
• (9x + 2)(3x² + 18x + 4)
• (3x²+4)(9x + 2)
• (27x + 8)(x² - 216x + 64)

Factor Completely:

343x³ - 27

• (7x² - 3)(7x+3)

• (7x - 3)(7x² + 21x + 9)

• (7x - 3)(49x² - 21x + 9)

• (7x - 3)(49x² + 21x + 9)

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

• 6, 3, -3
• -6, 3, -3
• -6, 3i, -3i
• 6, 3i, -3i

The degree of a polynomial determines...

• the maximum number of x-intercepts

• What Descartes' rule tells us

• Whether we factor or use the quadratic formula

• the y-intercept

How does a multiplicity of 2 affect the graph?

• cross

• bounce

• wiggle (change direction)

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.

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

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

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

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

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
• 2 (Mult of 3), 7 (mult 1)
• 0, 2, 7
• 2 (mult of 2), 7 (mult of 3)

Find the correct end behavior diagram for the given polynomial function.

 $f\left(x\right)=-x^6+9x^5-x^2-2x+3$  

• 
• 
• 
• 

Find the zeros of the polynomial function and state the multiplicity of each.

 $f\left(x\right)=x^3+6x^2-x-6$  

• -6, multiplicity 2 
  1, multiplicity 1

• -6, multiplicity 1 
  -1, multiplicity 1
  1, multiplicity 1

• -1, multiplicity 1
  1, multiplicity 1  
  6, multiplicity 1

• -6, multiplicity 1
  -1, multiplicity 2