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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 does the Factor Theorem state?

Please select an answer first.

Correct answer: A

The correct answer is If p(r)=0p(r)=0, then x−rx-r is a factor of p(x)p(x)..

  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 value r is a zero exactly when x - r is a factor of the polynomial.
  3. Check the result: The correct answer is If p(r)=0p(r)=0, then x−rx-r is a factor of p(x)p(x)..

A value r is a zero exactly when x - r is a factor of the polynomial.

2. QuestionMultiple choice

What is the remainder when p(x)=x2+4x+1p(x)=x^2+4x+1 is divided by x−2x-2?

Please select an answer first.

Correct answer: B

The correct answer is 13.

  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: Use the Remainder Theorem: p(2) = 2^2 + 4(2) + 1 = 13.
  3. Check the result: The correct answer is 13.

Use the Remainder Theorem: p(2) = 2^2 + 4(2) + 1 = 13.

3. QuestionMultiple choice

What is (2x2+3x−1)+(x2−5x+4)(2x^2+3x-1)+(x^2-5x+4)?

Please select an answer first.

Correct answer: C

The correct answer is 3x2−2x+33x^2-2x+3.

  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: Combine like terms: 2x^2 + x^2 = 3x^2, 3x - 5x = -2x, and -1 + 4 = 3.
  3. Check the result: The correct answer is 3x2−2x+33x^2-2x+3.

Combine like terms: 2x^2 + x^2 = 3x^2, 3x - 5x = -2x, and -1 + 4 = 3.

4. QuestionMultiple choice

What is the product x(x2−3x+2)x(x^2-3x+2)?

Please select an answer first.

Correct answer: D

The correct answer is x3−3x2+2xx^3-3x^2+2x.

  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: Distribute x to every term: x^3 - 3x^2 + 2x.
  3. Check the result: The correct answer is x3−3x2+2xx^3-3x^2+2x.

Distribute x to every term: x^3 - 3x^2 + 2x.

5. QuestionMultiple choice

Which is the factored form of x3−4xx^3-4x?

Please select an answer first.

Correct answer: A

The correct answer is x(x−2)(x+2)x(x-2)(x+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: Factor out x, then factor x^2 - 4 as (x - 2)(x + 2).
  3. Check the result: The correct answer is x(x−2)(x+2)x(x-2)(x+2).

Factor out x, then factor x^2 - 4 as (x - 2)(x + 2).

6. QuestionMultiple choice

What is synthetic division primarily used to divide by?

Please select an answer first.

Correct answer: B

The correct answer is A linear factor of the form x−rx-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: Synthetic division is a streamlined method for dividing by x - r and can reveal a quotient and remainder.
  3. Check the result: The correct answer is A linear factor of the form x−rx-r.

Synthetic division is a streamlined method for dividing by x - r and can reveal a quotient and remainder.

7. QuestionMultiple choice

If dividing p(x)p(x) by x+3x+3, which number is used in synthetic division?

Please select an answer first.

Correct answer: C

The correct answer is -3.

  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: Rewrite x + 3 as x - (-3), so the synthetic value is -3.
  3. Check the result: The correct answer is -3.

Rewrite x + 3 as x - (-3), so the synthetic value is -3.

8. QuestionMultiple choice

What does a zero of multiplicity 2 usually do on a polynomial graph?

Please select an answer first.

Correct answer: D

The correct answer is The graph touches the x-axis and turns around at that 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: Even multiplicity usually produces a bounce at the x-axis, while odd multiplicity usually produces a crossing.
  3. Check the result: The correct answer is The graph touches the x-axis and turns around at that zero..

Even multiplicity usually produces a bounce at the x-axis, while odd multiplicity usually produces a crossing.

9. QuestionMultiple choice

What is the result of multiplying a polynomial by a nonzero constant?

Please select an answer first.

Correct answer: A

The correct answer is The vertical scale and possibly reflection change, but the zeros stay the same..

  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 nonzero constant changes outputs but does not change where the polynomial equals zero.
  3. Check the result: The correct answer is The vertical scale and possibly reflection change, but the zeros stay the same..

A nonzero constant changes outputs but does not change where the polynomial equals zero.

10. QuestionMultiple choice

Why can factoring help solve a polynomial equation?

Please select an answer first.

Correct answer: B

The correct answer is It turns a product equal to zero into simpler equations using the zero-product property..

  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: If a product is zero, at least one factor is zero, allowing the equation to be solved factor by factor.
  3. Check the result: The correct answer is It turns a product equal to zero into simpler equations using the zero-product property..

If a product is zero, at least one factor is zero, allowing the equation to be solved factor by factor.

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