Polynomial Function Review

“ARE YOU READY FOR THIS?”

Student will be able to identify polynomial functions by degree.

1. Classify this polynomial by degree:f(x) = 4x³ + 2x² - 3x + 7

a. binomialb. 4 termc. cubicd. quartic

How do you know?

Student will be able to identify polynomial functions by degree.

2. Classify this polynomial by degree:f(x) =(x – 5i)(x + 5i)

a. binomialb. quadraticc. cubicd. quartic

How do you know?

Student will be able to identify polynomial functions by degree.

3. Classify the polynomial by degree if it has the following zeros: { 7, 1 mult. 2, -2}

a. binomialb. 4 termc. cubicd. quartic

How do you know?

Student will be able to identify polynomial functions by number of terms.

4.Classify this polynomial by number of terms:

f(x) = -2x³ + 2x² - 3x + 7a. trinomialb. 4 termc. cubicd. binomial

How do you know?

Student will be able to put polynomial functions in standard form.

5. Put this polynomial in standard form:

f(x) = -2x + 43 - 3x² + 7x⁵

a. f(x) = -2x + 43 - 3x² + 7x⁵b. f(x) = 43 -2x + - 3x² + 7x⁵c. f(x) = - 3x² -2x + 7x⁵ + 43d. f(x) = 7x⁵ - 3x² -2x + 43

How do you know?

Student will be able to identify the leading coefficient of a polynomial function.

6. Identify the leading coefficient of this polynomial:

f(x) = -2x³ + 2x² - 3x + 7a. 7b. -2xc. -2d. x

How do you know?

Student will be able to identify the leading coefficient of a polynomial function.

7. Identify the leading coefficient of this polynomial:

f(x) = -x² + 2x³ - 3x + 7a. -1b. 7c. 2d. x

How do you know?

Student will be able to identify the leading coefficient of a polynomial function.

8. Identify the leading coefficient of this polynomial:

f(x) = -x³ + 4x² - 3x + 7a. 7b. -x³c. 4d. -1

How do you know?

Student will be able to identify the end behavior of a polynomial function.9. Identify the end behavior of this polynomial:

f(x) = -x³ + 4x² - 3x + 7a. x -> -∞, y -> +∞ x -> +∞, y -> -∞

b. x -> -∞, y -> +∞ x -> +∞, y -> +∞

c. x -> -∞, y -> -∞ x -> +∞, y -> -∞

d. x -> -∞, y -> -∞ x -> +∞, y -> +∞

How do you know the right side?How do you know the left side?

Student will be able to write polynomial equations given real and/or complex roots.

10. Write the polynomial function with these roots in factored form: { 3 mult. 2, -4i }

a. f(x) = (x - 2)(x - 2)(x – 2)(x + 4i)b. f(x) = (x - 3)(x - 3)(x + 4i)(x – 4i)c. f(x) = (x + 3)(x + 3)(x + 4i)(x – 4i)d. f(x) = (x - 2)(x - 2)(x – 2)(x + 4i)(x – 4i)

How do you know?

Student will be able to write polynomial equations given real and/or complex roots.

11. Write the polynomial function with these factors in standard form: (x – 2)(x + 1)(x – 1)

a. f(x) = x³ - x² + x - 2b. f(x) = x³ - x² + x + 2c. f(x) = x³ - 2x² + x - 2d. f(x) = x³ - 2x² - x + 2

How do you know?

Student will be able to graph polynomial functions.

12. Identify the y-intercept of this polynomial function: f(x) = 3x⁵ - 2x³ + 17

a. 3b. 5c. There is no y-interceptd. 17

How do you know?

Student will be able to graph polynomial functions.

13. Identify the y-intercept of this polynomial function: f(x) = -6x⁵ - 12x³ + 17x

a. -6b. 0c. There is no y-interceptd. 17

How do you know?

Student will be able to divide polynomials with synthetic division.

14. Choose the correct way to set up a Synthetic Division of this polynomial: 3x⁴ + 5x³ - 2x + 3 - x⁵

x - 3a. -3 3 5 -2 3 -1

b. -3 -1 3 5 0 -2 3

c. 3 3 5 -2 3 -1

d. 3 -1 3 5 0 -2 3 Now solve it!

Student will be able to evaluate functions with synthetic division.

15. Evaluate f(4) if f(x) = 7x⁴ + 5x³ - 2x + 3 - x⁵

(Use synthetic division)a. f(4) = 2507

b. f(4) = 452

c. f(4) = 1083

d. f(4) = 2578

How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations.

16. Use a graphing calculator to find the zeros of this polynomial function: f(x) = -4x³ + x² - 3

a. -3b. -8c. -.83d. 5i

How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations.

17. Use a graphing calculator to find the relative extrema of this polynomial function:

f(x) = -4x³ + x² - 3

a. relative maximum at (-1, -3)b. relative minimum and maximum at (.6, -3.6)c. relative maximum at (2, -4)d. relative minimum at (3, -.6)

How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations.

18. Use a graphing calculator to find the y value of this polynomial function where x = 5:

f(x) = -4x³ + x² - 3

a. -3b. -478c. -5d. 3

How do you know?

Students will be able to describe the roots of polynomial functions.

19. How many roots does this polynomial have?

f(x) = 56x⁴ - 12x³ + 4x² - 3x + 1

a. 56b. 1c. 4d. 5

How do you know?

Students will be able to describe the roots of polynomial functions.

20. What are the possible rational roots of this polynomial?

f(x) = 6x⁴ - 12x³ + 4x² - 3x + 8

a. { ±8, ±6}

b. {± 1, ± 2, ±4, ± 8, ±1/6, ±1/2, ±1/3, ±2/3, ±4/3, ±8/3}

c. {± 1, ± 2, ±4, ± 6,± 8}

d. {1, 2, 4, 8, 1/6, 1/2, 1/3, 2/3, 4/3, 8/3}

How do you know?