Polynomial Graphing

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 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

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

• 5

• 4

• 3

• 2

• 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

Determine the y-intercept 
f(x) = x³ - 5x² - 25x + 125

• (0,0)

• (0,25)

• (0,125)

• (0,5)

What is the end-behavior of the function 
y = x⁶ - 7x⁵ + 7x - 9

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

What is the end-behavior of the function 
y = -x³ + 6x² + 7x

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

Match the following:

• The remainder is...

• x+2

• 5x² -10x - 40 is being divided by...

• x + 2...

• 0

• -2...

What is the proper way to write the answer for the following problem?

• 2x³-x²-25x+12

• 2x⁴-x³-25x²-12x+0

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x-0

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3