Grade 9 Polynomials worksheet
from Gradelings · Name: ______________________
How to explain it
- Like terms have the same variable and exponent. Only combine those.
- To add polynomials, combine like terms.
- To expand, multiply each term inside the brackets: a(b + c) = ab + ac.
Example: (3x + 2) + (x − 5) = ? Combine the x terms: 3x + x = 4x. Combine the numbers: 2 − 5 = −3. Answer: 4x − 3
Question 1
Classify the polynomial 9x² + 1 by its number of terms.
- binomial
- trinomial
- quadrinomial
- monomial
binomial
Hint: Count the terms: 9x² + 1 has 2. One term is a monomial, two a binomial, three a trinomial.
Question 2
What is the degree of 8x − 2?
answer box
1
Hint: The degree is the highest exponent on the variable.
Question 3
Add: (−3x² + 2x + 9) + (−2x² − x − 3)
- −5x² + x + 7
- −5x² + 2x + 6
- −5x² + x + 6
- −5x² + x − 4
- −5x² − x + 6
−5x² + x + 6
Hint: Add the like terms: -3 + (−2) = -5, 2 + (−1) = 1, 9 + (−3) = 6. The result is −5x² + x + 6.
Question 4
Subtract: (−9x² − 3x + 8) − (9x² + x + 1)
- −18x² − 5x + 7
- −18x² − 4x + 9
- −18x² − 4x + 7
- −2x + 9
- −18x² − 2x + 9
−18x² − 4x + 7
Hint: Subtracting a polynomial changes the sign of every term in it: −9x² − 3x + 8 + (−9x² − x − 1). Then combine like terms to get −18x² − 4x + 7.
Question 5
Expand: 4(−x² + 3x − 3)
- −4x² + 12x − 3
- −4x² − 14x − 12
- 3x² + 7x + 1
- −4x² + 3x − 3
- −4x² + 12x − 12
−4x² + 12x − 12
Hint: Multiply every term inside the brackets by 4: −4x² + 12x − 12.
Question 6
Divide: (−4x² − 4x − 24) ÷ 4
- −x² − x − 6
- −x² − x + 7
- −x² − 2x − 6
- −x² − 4x − 24
- −4x² − 4x − 6
−x² − x − 6
Hint: Divide every term by 4: -24, -4, -4 ÷ 4. The result is −x² − x − 6.
Question 7
Evaluate −3x² + 4x + 2 when x = 1.
answer box
3
Hint: Substitute x = 1: -3(1)² + 4(1) + 2 = -3 + 4 + 2 = 3.
Question 8
Which term is a like term of 8x²?
- 5x²
- 8x³
- 8y²
- 8x
5x²
Hint: Like terms have exactly the same variable raised to the same power. Only the coefficients can differ.
Question 9
Classify the polynomial 8x² by its number of terms.
- trinomial
- monomial
- quadrinomial
- binomial
monomial
Hint: Count the terms: 8x² has 1. One term is a monomial, two a binomial, three a trinomial.
Question 10
What is the degree of 4x² − x + 1?
answer box
2
Hint: The degree is the highest exponent on the variable.
Answer key
- 1. binomial
- 2. 1
- 3. −5x² + x + 6
- 4. −18x² − 4x + 7
- 5. −4x² + 12x − 12
- 6. −x² − x − 6
- 7. 3
- 8. 5x²
- 9. monomial
- 10. 2
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