A. 4𝑥 +12𝑥 +9𝑥 =0 . 𝑥 +2𝑥 −9𝑥−18=0...Write a polynomial function f of least #4 degree that has rational coefficients, a leading coefficient of 1, and the given

#1

Solve by factoring.

A. 4𝑥4 + 12𝑥3 + 9𝑥2 = 0

𝐵. 𝑥3 + 2𝑥2 − 9𝑥 − 18 = 0

𝐶. 3𝑥3 = 21𝑥

#2Sketch a graph of each of the functions.

A. 𝑓 𝑥 = 𝑥4 − 8𝑥2 + 16

𝐵. 𝑔 𝑥 = −3𝑥3 − 15𝑥2 − 12𝑥

#3

Consider each of the functions below and answer the questions on your worksheet.

A. 𝑓 𝑥 = 𝑥4 − 5𝑥2 − 36

𝐵. 𝑔 𝑥 = 𝑥3 + 3𝑥2 − 𝑥 − 1

#4Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

A. 2, 3

𝐵. −2, 3 + 𝑖

#5Complete the following table.

#6

Functionx-

interceptsLocal Max

Local Min

Increasing Decreasing Odd or Even?

𝑓 𝑥 = 2𝑥3 − 5𝑥2

𝑔 𝑥 = −𝑥4 + 2𝑥

ℎ 𝑥 = 𝑥4 − 4𝑥3 + 5𝑥 − 2

Match each graph with its equation.

Use finite differences to determine the degree of the polynomial function that fits the data. Use technology to find the model.

C. Find a polynomial model for the data.

#7

Write a cubic function whose graph passes through the given points.

A. B.

#8

For Answers

#1

Solve by factoring.

A. 4𝑥4 + 12𝑥3 + 9𝑥2 = 0

𝐵. 𝑥3 + 2𝑥2 − 9𝑥 − 18 = 0

𝐶. 3𝑥3 = 21𝑥

#2Sketch a graph of each of the functions.

A. 𝑓 𝑥 = 𝑥4 − 8𝑥2 + 16

𝐵. 𝑔 𝑥 = −3𝑥3 − 15𝑥2 − 12𝑥

#3

Consider each of the functions below and answer the questions on your worksheet.

A. 𝑓 𝑥 = 𝑥4 − 5𝑥2 − 36

i. How many solutions? __________

ii. How many REAL solutions? ________

iii. How many NON-REAL solutions? _______

iv. Find ALL the solutions.

𝐵. 𝑔 𝑥 = 𝑥3 + 3𝑥2 − 𝑥 − 1

i. How many solutions? __________

ii. How many REAL solutions? ________

iii. How many NON-REAL solutions? _______

iv. Find ALL the solutions.

#4Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

A. 2, 3

𝐵. −2, 3 + 𝑖

#5Complete the following table.

Function x-intercepts Local Max Local Min Increasing Decreasing

𝑓 𝑥 = 2𝑥3 − 5𝑥2

𝑔 𝑥 = −𝑥4 + 2𝑥

ℎ 𝑥 = 𝑥4 − 4𝑥3 + 5𝑥 − 2

#6Match each graph with its equation.

#7

Write a cubic function whose graph passes through the given points.

A.

B.

Use finite differences to determine the degree of the polynomial function that fits the data. Use technology to find the model.

c. Find a polynomial model for the data.

#8