Identify the roots of $$-3x^3-21x^2+72x+540=0$$ . State the multiplicity of each root.

x + 5 is a factor once, and x - 6 is a factor twice. The root -5 has a multiplicity of 1, and the root 6 has a multiplicity of 2.

x - 5 is a factor once, and x - 6 is a factor twice. The root 5 has a multiplicity of 1, and the root 6 has a multiplicity of 2.

x - 5 is a factor of P(x) twice, and x + 6 is a factor once. The root 5 has a multiplicity of 2, and the root -6 has a multiplicity of 1.

When P(x) is divided by x - r and the remainder is equal to 0, it means ____.

𝑥 − 𝑟 is a factor of 𝑃(𝑥)

𝑃(𝑥) is the only factor of 𝑥 − r

𝑃(𝑥) is a factor of 𝑥 − 𝑟

𝑥 − 𝑟 is the only factor of 𝑃(𝑥)

Identify the leading coefficient, degree, and the end behavior of the function $$P(x)=-5x^4+6x^2+6.$$

The leading coefficient is -5. The degree is 4. As x approaches negative infinity, P(x) approaches negative infinity and as x approaches positive infinity, P(x) approaches negative infinity.

The leading coefficient is -5. The degree is 6. As x approaches negative infinity, P(x) approaches negative infinity and as x approaches positive infinity, P(x) approaches negative infinity.

The leading coefficient is -5. The degree is 4. As x approaches negative infinity, P(x) approaches positive infinity and as x approaches positive infinity, P(x) approaches positive infinity.

The leading coefficient is -5. The degree is 6. As x approaches negative infinity, P(x) approaches positive infinity and as x approaches positive infinity, P(x) approaches positive infinity.

Which of the following is NOT true about the graph?

The f(x) is positive when x > 9.

The graph of $$f\left(x\right)=-x^4+3x^3+2x^2-5x-4$$ is provided. Describe and identify the number of real zeros.

From left to right, the graph alternately increases and decreases, changing direction three times. It crosses the x-axis two times, so there appear to be two real zeros.

From left to right, the graph alternately increases and decreases, changing direction two times. It crosses the x-axis three times, so there appear to be three real zeros.

From left to right, the graph increases and then decreases. It crosses the x-axis twice, so there appear to be two real zeros.

. From left to right, the graph alternately increases and decreases, changing direction three times. It crosses the x-axis four times, so there appear to be four real zeros

Which of the ff is a true statement about the graph of $$p\left(x\right)=\left(x-4\right)\left(x+2\right)\left(3x^2+6x\right)?$$

The graph crosses the x-axis two times and is tangent to the x-axis once.

The graph crosses the x-axis four times and is never tangent to the x-axis.

The graph crosses the x-axis three times and is never tangent to the x-axis.

The graph crosses the x-axis three times and is tangent to the x-axis once.

On which step did she potentially make an algebraic error?

Jessica didn’t expand (x + yi)(x - yi) correctly in Step 1

Jessica incorrectly combined the terms in Step 2.

It is impossible to prove because the original identity is false.

Are each of his steps valid? If not, in which step is there an error?

All of Vincent’s steps are valid.

Vincent didn’t correctly expand the binomial in Step 1.

Vincent can’t just add to the expression in Step 2.

Vincent factored incorrectly the terms in Step 4.

What are the extrema of the graph?

Max = (-3, 2), (2, 1) Min = (-1, -3), (4, -1)

Max = (2, -3), (1, 2) Min = (-3, -1), (-1, 4)

Max = (-3, -1), (-1, 4) Min = (2, -3), (1, 2)

Max = (-1, -3), (4, -1) Min = (-3, 2), (2, 1)

A fifth degree polynomial function is shown below. Which of the statements are NOT true about this function?

Leading coefficient is positive

Positive from x = -2 to x = 1.75

When g(x) is divided by x + 4, the remainder is 0. Given $$g(x)=x^4+3x^3−6x^2−6x+8$$ , which conclusion about g(x) is true?

No conclusion can be made regarding g(x)

MAJOR ASSESSMENT #4: Unit 3

Authored by Kathy Binondo

Mathematics

12th Grade

Used 11+ times

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

An integer

A non-negative integer

Any integer

Any number except zero

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which of the following is NOT an example of a polynomial equation?

MATH RESPONSE QUESTION

5 mins • 1 pt

Mathematical Equivalence

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which of the following illustrates a quartic equation?

x - 7 = 0

MATH RESPONSE QUESTION

5 mins • 1 pt

Mathematical Equivalence

OFF

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which of the following is correct about the degree of a polynomial?

Largest coefficient of x

Smallest coefficient of x

Highest power of x

Lowest power of x

MATH RESPONSE QUESTION

5 mins • 1 pt

Mathematical Equivalence

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MAJOR ASSESSMENT #4: Unit 3

Which of the following is NOT an example of a polynomial equation?

Which of the following illustrates a quartic equation?

Which of the following is correct about the degree of a polynomial?

Which is a third degree polynomial with -3 and 2 as its only zeros?

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