Polynomial Rational and Radical Relationships Practice Questions

Common Core (US) · Common Core Algebra 2 · 144 free MCQs with instant results and detailed explanations.

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Sample Questions from Polynomial Rational and Radical Relationships

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Easy

What is the degree of the polynomial expression 3x^4 - 5x^3 + 2x - 7?

A. 4

B. 3

C. 2

D. 1

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Correct Answer: A

The degree of a polynomial is the highest power of the variable. In this expression, the highest power is 4 (from 3x^4).

Easy

Which of the following is a correct factorization of the polynomial x^2 - 9?

A. (x - 3)(x + 3)

B. (x - 9)(x + 1)

C. (x - 3)(x - 3)

D. (x + 9)(x + 1)

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Correct Answer: A

The expression x^2 - 9 is a difference of squares, which can be factored as (x - 3)(x + 3).

Easy

What is the degree of the polynomial function f(x) = 4x^3 - 2x^2 + 5?

A. 3

B. 2

C. 5

D. 1

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Correct Answer: A

The degree of a polynomial is the highest power of x in the expression. In f(x), the highest power is x^3, which makes the degree 3.

Medium

What is the degree of the polynomial function f(x) = 4x^3 - 2x^2 + 5x - 7?

A. 3

B. 2

C. 4

D. 1

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Correct Answer: A

The degree of a polynomial is determined by the highest power of the variable. In this case, the term with the highest exponent is 4x^3, which has a degree of 3.

Medium

Which of the following expressions is equivalent to (x^2 - 4)/(x + 2)?

A. x - 2

B. x + 2

C. x^2 + 2

D. x - 4

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Correct Answer: A

The expression (x^2 - 4) can be factored as (x - 2)(x + 2), so when divided by (x + 2), it simplifies to (x - 2).

Medium

What is the solution to the equation x^2 - 5x + 6 = 0?

A. x = 2 or x = 3

B. x = -2 or x = -3

C. x = 0 or x = 6

D. x = 1 or x = 6

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Correct Answer: A

The quadratic factors as (x - 2)(x - 3) = 0, leading to solutions x = 2 and x = 3.

Medium

Which of the following is a rational function?

A. f(x) = (2x + 1)/(x^2 - 4)

B. f(x) = 2x + 1

C. f(x) = sqrt(x + 1)

D. f(x) = 1/x^2 + 2

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Correct Answer: A

A rational function is defined as the quotient of two polynomials. Here, (2x + 1) is a polynomial and (x^2 - 4) is also a polynomial, making this a rational function.

Hard

What is the value of x in the equation 3x^2 - 12x + 9 = 0?

A. 1

B. 3

C. 4

D. 5

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Correct Answer: B

To solve 3x^2 - 12x + 9 = 0, we can use the quadratic formula. Here, a = 3, b = -12, and c = 9. Plugging into the formula gives x = (12 ± √(144 - 108)) / 6 = (12 ± 6) / 6. Thus, x = 3 or x = 1, but the only solution that fits the standard form is x = 3.

Hard

If f(x) = (2x^2 - 8)/(x - 2), what is the domain of the function f(x)?

A. x ∈ ℝ, x ≠ 2

B. x ∈ ℝ

C. x > 2

D. x < 2

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Correct Answer: A

The function is undefined when the denominator is zero, which occurs at x = 2. Therefore, the domain excludes 2.

Q10

Hard

Which of the following expressions is equivalent to 3√(x^6y^3) when fully simplified?

A. 3x^2√(y)

B. 3x^2y√(y)

C. x^2y√(3)

D. 3x^2y

Show Answer & Explanation

Correct Answer: A

To simplify 3√(x^6y^3), we can write it as 3(x^2√(x^0)y√(y)), leading to 3x^2√(y).

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Polynomial Rational and Radical Relationships — Common Core (US) Common Core Algebra 2 Practice Questions Online

This page contains 144 practice MCQs for the chapter Polynomial Rational and Radical Relationships in Common Core (US) Common Core Algebra 2. The questions are organized by difficulty — 41 easy, 75 medium, 28 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.