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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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5 Tests
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1. Test

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 degree of p(x)=7x6−2x+1p(x)=7x^6-2x+1?

Please select an answer first.

Correct answer: A

The correct answer is 6.

  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 is the greatest exponent of x with a nonzero coefficient, which is 6.
  3. Check the result: The correct answer is 6.

The degree is the greatest exponent of x with a nonzero coefficient, which is 6.

2. QuestionMultiple choice

What is the leading coefficient of p(x)=−4x3+2x2−1p(x)=-4x^3+2x^2-1?

Please select an answer first.

Correct answer: B

The correct answer is -4.

  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 leading term is -4x^3, so the leading coefficient is -4.
  3. Check the result: The correct answer is -4.

The leading term is -4x^3, so the leading coefficient is -4.

3. QuestionMultiple choice

What is p(2)p(2) for p(x)=x3−2x+5p(x)=x^3-2x+5?

Please select an answer first.

Correct answer: C

The correct answer is 9.

  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: Substitute x = 2: 2^3 - 2(2) + 5 = 8 - 4 + 5 = 9.
  3. Check the result: The correct answer is 9.

Substitute x = 2: 2^3 - 2(2) + 5 = 8 - 4 + 5 = 9.

4. QuestionMultiple choice

Which value is a zero of p(x)=x−8p(x)=x-8?

Please select an answer first.

Correct answer: D

The correct answer is 8.

  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 makes the polynomial equal to zero: 8 - 8 = 0.
  3. Check the result: The correct answer is 8.

A zero makes the polynomial equal to zero: 8 - 8 = 0.

5. QuestionMultiple choice

What is the constant term of 3x4−5x+93x^4-5x+9?

Please select an answer first.

Correct answer: A

The correct answer is 9.

  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 constant term is the term with no variable, which is 9.
  3. Check the result: The correct answer is 9.

The constant term is the term with no variable, which is 9.

6. QuestionMultiple choice

What is the maximum number of real zeros of a degree-5 polynomial?

Please select an answer first.

Correct answer: B

The correct answer is 5.

  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 degree-n polynomial can have at most n real zeros, so degree 5 allows at most 5.
  3. Check the result: The correct answer is 5.

A degree-n polynomial can have at most n real zeros, so degree 5 allows at most 5.

7. QuestionMultiple choice

What is the end behavior of an odd-degree polynomial with a positive leading coefficient?

Please select an answer first.

Correct answer: C

The correct answer is The left end falls and the right end rises..

  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: Odd degree gives opposite end directions; a positive leading coefficient makes the right end rise.
  3. Check the result: The correct answer is The left end falls and the right end rises..

Odd degree gives opposite end directions; a positive leading coefficient makes the right end rise.

8. QuestionMultiple choice

What is the end behavior of an even-degree polynomial with a negative leading coefficient?

Please select an answer first.

Correct answer: D

The correct answer is Both ends fall..

  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: Even degree gives matching directions, and a negative leading coefficient makes both ends fall.
  3. Check the result: The correct answer is Both ends fall..

Even degree gives matching directions, and a negative leading coefficient makes both ends fall.

9. QuestionMultiple choice

What does the Fundamental Theorem of Algebra guarantee?

Please select an answer first.

Correct answer: A

The correct answer is A degree-n polynomial has n complex zeros counted with multiplicity..

  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 counts all complex roots, including repeated roots, and gives the total equal to the degree.
  3. Check the result: The correct answer is A degree-n polynomial has n complex zeros counted with multiplicity..

The theorem counts all complex roots, including repeated roots, and gives the total equal to the degree.

10. QuestionMultiple choice

What is the y-intercept of p(x)=2x3−4x+6p(x)=2x^3-4x+6?

Please select an answer first.

Correct answer: B

The correct answer is 6.

  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 y-intercept occurs at x = 0, so p(0) = 6.
  3. Check the result: The correct answer is 6.

The y-intercept occurs at x = 0, so p(0) = 6.

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