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Exponents and Polynomials Practice Tests

These Grade 9 Math practice tests cover positive, zero, and negative exponents, products and quotients of powers, powers of powers, scientific notation, monomials, polynomial degree and coefficients, polynomial addition and subtraction, multiplication, factoring, and algebraic models.

Skills covered

  • Applying product, quotient, power, and negative-exponent rules
  • Evaluating powers and rewriting expressions with positive exponents
  • Identifying degree, leading coefficient, constant term, and like terms
  • Adding, subtracting, multiplying, and factoring polynomials
  • Using polynomial expressions for area, volume, functions, sequences, and scientific notation

How to use these practice tests

Identify matching bases before applying exponent rules, combine only like terms, distribute to every term, and check polynomial products by substituting a simple value when needed.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Exponents and Polynomials Practice Tests

Practice Grade 9 Math questions about exponent rules, zero and negative exponents, monomials, polynomial degree, polynomial operations, factoring, and algebraic models.

Choose the best answer. Apply exponent rules, combine like terms, distribute carefully, write polynomials in standard form, and check equivalent expressions.

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

What is the degree of 4x3+2x−14x^3+2x-1?

Please select an answer first.

Correct answer: A

The correct answer is 3.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The degree is the greatest exponent of the variable, which is 3.
  3. Check equivalent form: The correct choice is 3.

The degree is the greatest exponent of the variable, which is 3.

2. QuestionMultiple choice

Which pair contains like terms?

Please select an answer first.

Correct answer: B

The correct answer is 3x23x^2 and −5x2-5x^2.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Like terms have identical variable parts and exponents, so 3x squared and -5x squared are like terms.
  3. Check equivalent form: The correct choice is 3x23x^2 and −5x2-5x^2.

Like terms have identical variable parts and exponents, so 3x squared and -5x squared are like terms.

3. QuestionMultiple choice

Add (2x+3)+(5x−1)(2x+3)+(5x-1)

Please select an answer first.

Correct answer: C

The correct answer is 7x+27x+2.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Combine x terms and constants: 2x + 5x = 7x and 3 - 1 = 2.
  3. Check equivalent form: The correct choice is 7x+27x+2.

Combine x terms and constants: 2x + 5x = 7x and 3 - 1 = 2.

4. QuestionMultiple choice

Subtract (2x2−3x+1)(2x^2-3x+1) from (6x2+x)(6x^2+x)

Please select an answer first.

Correct answer: D

The correct answer is 4x2+4x−14x^2+4x-1.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Distribute the subtraction: 6x squared + x - 2x squared + 3x - 1 = 4x squared + 4x - 1.
  3. Check equivalent form: The correct choice is 4x2+4x−14x^2+4x-1.

Distribute the subtraction: 6x squared + x - 2x squared + 3x - 1 = 4x squared + 4x - 1.

5. QuestionMultiple choice

Simplify (4a2−3a+1)+(2a2+5a−7)(4a^2-3a+1)+(2a^2+5a-7)

Please select an answer first.

Correct answer: A

The correct answer is 6a2+2a−66a^2+2a-6.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Combine like terms: 4a squared + 2a squared, -3a + 5a, and 1 - 7.
  3. Check equivalent form: The correct choice is 6a2+2a−66a^2+2a-6.

Combine like terms: 4a squared + 2a squared, -3a + 5a, and 1 - 7.

6. QuestionMultiple choice

Write 3+2x2−x3+2x^2-x in standard form.

Please select an answer first.

Correct answer: B

The correct answer is 2x2−x+32x^2-x+3.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Standard form lists terms in descending powers of the variable.
  3. Check equivalent form: The correct choice is 2x2−x+32x^2-x+3.

Standard form lists terms in descending powers of the variable.

7. QuestionMultiple choice

What is the coefficient of x2x^2 in −4x2+7x-4x^2+7x?

Please select an answer first.

Correct answer: C

The correct answer is -4.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The coefficient is the numerical factor multiplying x squared, which is -4.
  3. Check equivalent form: The correct choice is -4.

The coefficient is the numerical factor multiplying x squared, which is -4.

8. QuestionMultiple choice

What is the constant term in 5x3−2x+95x^3-2x+9?

Please select an answer first.

Correct answer: D

The correct answer is 9.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The constant term has no variable, so it is 9.
  3. Check equivalent form: The correct choice is 9.

The constant term has no variable, so it is 9.

9. QuestionMultiple choice

Simplify x2−x2x^2-x^2

Please select an answer first.

Correct answer: A

The correct answer is 0.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Subtracting identical terms gives zero.
  3. Check equivalent form: The correct choice is 0.

Subtracting identical terms gives zero.

10. QuestionMultiple choice

What is the leading coefficient of 7x4−3x2+x−17x^4-3x^2+x-1?

Please select an answer first.

Correct answer: B

The correct answer is 7.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The leading term is 7x to the fourth, so its coefficient is 7.
  3. Check equivalent form: The correct choice is 7.

The leading term is 7x to the fourth, so its coefficient is 7.

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