Circuit The polynomial Function PDF

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Class work notes about the nucleus and mass...

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Circuit Training – The Polynomial Function

Name __________________________

Directions: Begin in cell 1. Without a calculator, determine the answer. Show your work – this may require separate paper. Circle your answer and search for it. This will become #2. Proceed in this manner until you complete the circuit. # ___1___

Answer: 17

What is the degree of the polynomial function 𝑦 = −(𝑥 − 4)(𝑥 2 − 3)2 ?

# _______

Answer: −2

Where is the graph of 𝑦 = −𝑥 2 + 2𝑥 decreasing and concave up?

# _____

Answer: −8

If you know that 2 − √5 is a root of 𝑤(𝑥), then you know that 2 + 𝑎 is also a root. What is 𝑎 ?

# _______

Answer: 0

Find the largest zero of the polynomial function 𝑓(𝑥) = 2𝑥 3 − 2𝑥 2 − 6𝑥 + 6.

If the answer is… (−∞, 1) … go to – 8. If the answer is… (1, ∞) … go to – 1. If the answer is… (−∞, ∞) … go to −9. If the answer is… nowhere … go to −10.

# _______

Answer: 5

Luna wrote a quartic trinomial on the board. What was its degree?

# _______

Answer: √3

Polynomials always have a(n) ____________ number of imaginary roots. If the answer is even… go to √6. If the answer is odd… go to √5.

# _______

Answer: −15

Any cubic polynomial has a minimum of how many 𝑥 − intercepts?

# _______.

Answer: −9

You may use your graphing calculator on only this question! Use it to examine the graph of 𝑝(𝑥) = −2𝑥(𝑥 − 3)3 . Rounded to the nearest whole number, what is the maximum value of 𝑝(𝑥) ?

© Virge Cornelius 2021 for Kathy Stevens and her students!

# _______

Answer: 8

# _____

Answer: 4

Polly put a sixth degree polynomial into her calculator. What is the minimum number of 𝑥 − intercepts it could have?

What is the 𝑦 −intercept of the graph of the 1 quadratic function 𝑦 = 2 (𝑥 − 6)(𝑥 + 5) ?

# _______

# _______

Answer: 1

One of the roots of 𝑦 = 2𝑥 3 − 15𝑥 2 + 22𝑥 + 15 1 is − 2 . Find the sum of the other roots.

# _______

Answer : −10

The polynomial 2𝑥 3 − 9𝑥 2 + 7𝑥 + 6 can be factored as (2𝑥 + 𝑎 )(𝑥 + 𝑏)(𝑥 − 2). What is 5𝑎 + 2𝑏?

Answer: √6

When 𝑔(𝑥) = 4𝑥 3 + 2𝑘𝑥 + 1 is divided by 𝑥 + 2 the remainder is 13. Find 𝑘.

Answer: −1

# _______ 2

Is a possible rational root of 3 ℎ(𝑥) = 3𝑥 4 − 5𝑥 3 − 𝑥 2 + 𝑥 + 4? If yes, go to −8. If no, go to −9.

# _______

Answer: –11

𝑃(𝑥) is a cubic polynomial with two roots. The roots are 𝑥 = 1 and 𝑥 = −3 where 𝑥 = −3 has a multiplicity of two. 𝑃(0) = −6. What is 𝑃(−2)?

Answer: √5

# _______.

The table gives selected values of the function 𝑦 = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑. What is 𝑎 + 𝑑 ? 𝑥 𝑦

© Virge Cornelius 2021 for Kathy Stevens and her students!

–2 36

–1 0

0 –6

1 0

2 0

3 – 24...