Polynomial Attributes and Characteristics

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph. Determine the end behavior of the polynomial.

f(x) = 2x³ - x + 5

• Left up Right up

• Left up Right down

• Left down Right up

• Left down Right down

Determine the end behavior of the polynomial by identifying the degree and leading coefficient.

f(x) = 5x⁴ - x + 6

• UP-UP

• UP-DOWN

• DOWN-UP

• DOWN-DOWN

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)

f(x)=(x+4)(x-3)(x-2)

List the zeros for this function.

• x = -4, x = 3, x = -2

• x = -4, x = 3, x = 2

• x = -4, x = -3, x = 2

• x = 4, x = 3, x = 2

What are the zeros of the graph?

• -4, -1, 2, 1 multiplicity 2

• -4, -1, 1, 2

• 4, 1, -2, -1 multiplicity 2

• 4, 1, -1, -2

Which is a zero of the graph?

• 0

• -1

• 1.5

• -3

Which of the following can you use to help you determine the end behavior of a polynomial's graph?

• The number of terms

• The degree

• The constant term

• The leading coefficient

A polynomial of degree n will have at most how many extrema (max/min)?

• n − 1

• n + 1

• n

• n/2

Describe the end behavior of the graph.

• x → ∞, y→ ∞ and x→∞, y→⁻∞

• x → ∞, y→ ∞ and x→⁻∞, y→∞

• x → ∞, y→ ∞ and x→⁻∞, y→ 0

• x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

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)