NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

4. Test

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

Multiply 3x2⋅4x33x^2\cdot4x^3

Please select an answer first.

Correct answer: A

The correct answer is 12x512x^5.

  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: Multiply coefficients 3 × 4 and add exponents 2 + 3 to get 12x to the fifth.
  3. Check equivalent form: The correct choice is 12x512x^5.

Multiply coefficients 3 × 4 and add exponents 2 + 3 to get 12x to the fifth.

2. QuestionMultiple choice

Expand 5(2x−3)5(2x-3)

Please select an answer first.

Correct answer: B

The correct answer is 10x−1510x-15.

  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 5 to both terms: 5(2x) - 5(3) = 10x - 15.
  3. Check equivalent form: The correct choice is 10x−1510x-15.

Distribute 5 to both terms: 5(2x) - 5(3) = 10x - 15.

3. QuestionMultiple choice

Expand x(x+7)x(x+7)

Please select an answer first.

Correct answer: C

The correct answer is x2+7xx^2+7x.

  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: Multiply x by each term: x squared + 7x.
  3. Check equivalent form: The correct choice is x2+7xx^2+7x.

Multiply x by each term: x squared + 7x.

4. QuestionMultiple choice

Expand (x+2)(x+3)(x+2)(x+3)

Please select an answer first.

Correct answer: D

The correct answer is x2+5x+6x^2+5x+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: Use the distributive property: x squared + 3x + 2x + 6 = x squared + 5x + 6.
  3. Check equivalent form: The correct choice is x2+5x+6x^2+5x+6.

Use the distributive property: x squared + 3x + 2x + 6 = x squared + 5x + 6.

5. QuestionMultiple choice

Expand (2x−1)(x+4)(2x-1)(x+4)

Please select an answer first.

Correct answer: A

The correct answer is 2x2+7x−42x^2+7x-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: Multiply each term: 2x squared + 8x - x - 4 = 2x squared + 7x - 4.
  3. Check equivalent form: The correct choice is 2x2+7x−42x^2+7x-4.

Multiply each term: 2x squared + 8x - x - 4 = 2x squared + 7x - 4.

6. QuestionMultiple choice

Expand (x−5)2(x-5)^2

Please select an answer first.

Correct answer: B

The correct answer is x2−10x+25x^2-10x+25.

  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: Use the square pattern: x squared - 2(5)x + 25.
  3. Check equivalent form: The correct choice is x2−10x+25x^2-10x+25.

Use the square pattern: x squared - 2(5)x + 25.

7. QuestionMultiple choice

Simplify (x+3)(x−3)(x+3)(x-3)

Please select an answer first.

Correct answer: C

The correct answer is x2−9x^2-9.

  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: This is a difference of squares: x squared minus 3 squared = x squared - 9.
  3. Check equivalent form: The correct choice is x2−9x^2-9.

This is a difference of squares: x squared minus 3 squared = x squared - 9.

8. QuestionMultiple choice

Factor 6x2+9x6x^2+9x

Please select an answer first.

Correct answer: D

The correct answer is 3x(2x+3)3x(2x+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 greatest common factor is 3x, leaving 2x + 3.
  3. Check equivalent form: The correct choice is 3x(2x+3)3x(2x+3).

The greatest common factor is 3x, leaving 2x + 3.

9. QuestionMultiple choice

Factor x2+5x+6x^2+5x+6

Please select an answer first.

Correct answer: A

The correct answer is (x+2)(x+3)(x+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: The numbers 2 and 3 multiply to 6 and add to 5.
  3. Check equivalent form: The correct choice is (x+2)(x+3)(x+2)(x+3).

The numbers 2 and 3 multiply to 6 and add to 5.

10. QuestionMultiple choice

Evaluate p(x)=x2−3x+4p(x)=x^2-3x+4 at x = 2.

Please select an answer first.

Correct answer: B

The correct answer is 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: Substitute 2: 2 squared - 3(2) + 4 = 4 - 6 + 4 = 2.
  3. Check equivalent form: The correct choice is 2.

Substitute 2: 2 squared - 3(2) + 4 = 4 - 6 + 4 = 2.

Previous testNext test