Grade 9 · Math · Unit 5 of 7
Polynomials
Add, subtract, expand and evaluate
What your child practises
Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.
Saskatchewan Curriculum outcome: P9.4 · polynomials of degree two or less
How we explain it
Children can open this short lesson before they practise.
- 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
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Classify the polynomial 2x² + 9 by its number of terms.
- quadrinomial
- binomial
- trinomial
- monomial
Show answer
binomial
Hint: Count the terms: 2x² + 9 has 2. One term is a monomial, two a binomial, three a trinomial.
Question 2
What is the degree of 7x − 3?
answer box
Show answer
1
Hint: The degree is the highest exponent on the variable.
Question 3
Add: (9x² + x + 7) + (9x² − 6x − 6)
- 18x² − 5x − 3
- 18x² − 4x + 1
- 19x² − 5x + 1
- 18x² − 5x + 1
- 16x² − 5x + 1
Show answer
18x² − 5x + 1
Hint: Add the like terms: 9 + 9 = 18, 1 + (−6) = -5, 7 + (−6) = 1. The result is 18x² − 5x + 1.
Question 4
Subtract: (−9x² − x + 3) − (9x² − 9x − 3)
- −18x² + 8x + 7
- −18x² − 10x
- −18x² + 8x − 7
- −10x
- −18x² + 8x + 6
Show answer
−18x² + 8x + 6
Hint: Subtracting a polynomial changes the sign of every term in it: −9x² − x + 3 + (−9x² + 9x + 3). Then combine like terms to get −18x² + 8x + 6.
Question 5
Expand: 5(x² − x − 4)
- 6x² + 4x + 1
- 5x² + 3x − 20
- 5x² − 5x − 4
- 5x² − x − 4
- 5x² − 5x − 20
Show answer
5x² − 5x − 20
Hint: Multiply every term inside the brackets by 5: 5x² − 5x − 20.
Question 6
Divide: (10x² + 6x + 6) ÷ 2
- 5x² + 2x + 3
- 5x² + 6x + 6
- 5x² + 3x + 3
- 10x² + 6x + 3
- 5x² + 4x + 3
Show answer
5x² + 3x + 3
Hint: Divide every term by 2: 6, 6, 10 ÷ 2. The result is 5x² + 3x + 3.