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Polynomial Functions Practice Tests

These Grade 11 Math practice tests develop polynomial function skills across degree, coefficients, evaluation, factoring, zeros, synthetic division, graph behavior, multiplicity, complex roots, and real-world modeling.

Skills covered

  • Identifying degree, leading coefficient, constant term, intercepts, zeros, maximum zeros, and end behavior
  • Using the Factor Theorem, Remainder Theorem, synthetic division, factoring, and the zero-product property
  • Interpreting polynomial graphs through x-intercepts, multiplicity, turning points, transformations, and end behavior
  • Building and evaluating polynomial models through interpolation, extrapolation, residuals, domain, units, and reasonableness
  • Applying the Rational Root Theorem, complex conjugate roots, discriminants, and verification strategies

How to use these practice tests

Start with the degree and leading term, then find factors or zeros and connect them to the graph. Keep multiplicity and domain restrictions visible, and check model answers against the real-world context.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Polynomial Functions Practice Tests

Practice Grade 11 Math questions about polynomial degree, coefficients, zeros, factors, synthetic division, multiplicity, graph behavior, complex roots, and polynomial modeling.

Choose the best answer. Use factoring, the Factor and Remainder Theorems, graph features, multiplicity, end behavior, and contextual checks to analyze each polynomial.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the Rational Root Theorem used to find?

Please select an answer first.

Correct answer: A

The correct answer is Possible rational zeros of a polynomial with integer coefficients.

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: The theorem provides candidates formed from factors of the constant term over factors of the leading coefficient.
  3. Check the result: The correct answer is Possible rational zeros of a polynomial with integer coefficients.

The theorem provides candidates formed from factors of the constant term over factors of the leading coefficient.

2. QuestionMultiple choice

If a polynomial has real coefficients and 2+i2+i is a zero, what else must be a zero?

Please select an answer first.

Correct answer: B

The correct answer is 2−i2-i.

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: Complex zeros of polynomials with real coefficients occur in conjugate pairs.
  3. Check the result: The correct answer is 2−i2-i.

Complex zeros of polynomials with real coefficients occur in conjugate pairs.

3. QuestionMultiple choice

How can a polynomial with known zeros be built?

Please select an answer first.

Correct answer: C

The correct answer is Multiply factors of the form x−rx-r for each zero r..

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: A zero r corresponds to a factor x - r, and multiplying the factors creates a polynomial with those roots.
  3. Check the result: The correct answer is Multiply factors of the form x−rx-r for each zero r..

A zero r corresponds to a factor x - r, and multiplying the factors creates a polynomial with those roots.

4. QuestionMultiple choice

What is the solution set of (x−3)(x+2)=0(x-3)(x+2)=0?

Please select an answer first.

Correct answer: D

The correct answer is x=3x=3 or x=−2x=-2.

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: By the zero-product property, x - 3 = 0 or x + 2 = 0.
  3. Check the result: The correct answer is x=3x=3 or x=−2x=-2.

By the zero-product property, x - 3 = 0 or x + 2 = 0.

5. QuestionMultiple choice

How many nonreal complex zeros does x2+4=0x^2+4=0 have?

Please select an answer first.

Correct answer: A

The correct answer is 2.

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: The equation gives x^2 = -4, so x = 2i or x = -2i, two nonreal zeros.
  3. Check the result: The correct answer is 2.

The equation gives x^2 = -4, so x = 2i or x = -2i, two nonreal zeros.

6. QuestionMultiple choice

What does the discriminant tell you about a quadratic?

Please select an answer first.

Correct answer: B

The correct answer is The number and type of its roots.

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: The discriminant distinguishes two real roots, one repeated real root, or two complex conjugate roots.
  3. Check the result: The correct answer is The number and type of its roots.

The discriminant distinguishes two real roots, one repeated real root, or two complex conjugate roots.

7. QuestionMultiple choice

What is the relationship between a polynomial's zeros and x-intercepts?

Please select an answer first.

Correct answer: C

The correct answer is Real zeros give the x-values of x-intercepts..

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: A real zero produces a point where the graph meets the x-axis; nonreal zeros are not real-plane intercepts.
  3. Check the result: The correct answer is Real zeros give the x-values of x-intercepts..

A real zero produces a point where the graph meets the x-axis; nonreal zeros are not real-plane intercepts.

8. QuestionMultiple choice

Why can a polynomial have fewer real zeros than its degree?

Please select an answer first.

Correct answer: D

The correct answer is Some zeros may be complex or repeated..

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: The degree counts complex roots with multiplicity, while a graph may show fewer distinct real zeros.
  3. Check the result: The correct answer is Some zeros may be complex or repeated..

The degree counts complex roots with multiplicity, while a graph may show fewer distinct real zeros.

9. QuestionMultiple choice

What is a good way to verify a proposed polynomial zero?

Please select an answer first.

Correct answer: A

The correct answer is Substitute the value into the original polynomial and check that the result is zero..

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: Direct substitution confirms whether the candidate actually satisfies p(x) = 0.
  3. Check the result: The correct answer is Substitute the value into the original polynomial and check that the result is zero..

Direct substitution confirms whether the candidate actually satisfies p(x) = 0.

10. QuestionMultiple choice

What is the best overall strategy for analyzing a polynomial function?

Please select an answer first.

Correct answer: B

The correct answer is Combine algebraic factoring or division with graph features, roots, multiplicity, and end behavior..

  1. Identify the polynomial feature: Determine whether the question asks about degree, coefficients, zeros, factors, multiplicity, end behavior, division, or modeling.
  2. Apply the polynomial relationship: Multiple representations provide a more complete and reliable analysis than one feature alone.
  3. Check the result: The correct answer is Combine algebraic factoring or division with graph features, roots, multiplicity, and end behavior..

Multiple representations provide a more complete and reliable analysis than one feature alone.

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