9th grade · Math · Unit 2 of 17
Polynomials
Add, subtract, expand and evaluate
What your child practices
Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.
Maine Learning Results learning standard: HSA.APR.A.1 · adding, subtracting and multiplying polynomials
How we explain it
Children can open this short lesson before they practice.
- 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
Polynomials in Maine
In the Maine Learning Results, this is unit 2 of 17 in 9th grade Math, after Exponents & Powers and before Multi-Step Equations.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Maine Department of Education
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 8x² by its number of terms.
- trinomial
- quadrinomial
- binomial
- monomial
monomial
Hint: Count the terms: 8x² has 1. One term is a monomial, two a binomial, three a trinomial.
Question 2
What is the degree of 7x − 9?
answer box
1
Hint: The degree is the highest exponent on the variable.
Question 3
Add: (2x² − 9x + 3) + (5x² + x + 1)
- 7x² − 8x − 6
- 8x² − 8x + 4
- 7x² − 8x + 4
- 7x² − 8x + 3
- 6x² − 8x + 4
7x² − 8x + 4
Hint: Add the like terms: 2 + 5 = 7, -9 + 1 = -8, 3 + 1 = 4. The result is 7x² − 8x + 4.
Question 4
Subtract: (−6x² − 3x + 4) − (−4x² + x − 5)
- −4x² − 4x + 9
- −2x² − 2x − 1
- −10x² − 2x − 1
- −2x² − 4x + 9
- −2x² − 4x + 8
−2x² − 4x + 9
Hint: Subtracting a polynomial changes the sign of every term in it: −6x² − 3x + 4 + (4x² − x + 5). Then combine like terms to get −2x² − 4x + 9.
Question 5
Expand: −4(6x² + 5x + 6)
- −24x² − 20x − 24
- −22x² − 20x − 24
- 2x² + x + 2
- −24x² + 5x + 6
- −24x² − 20x + 6
−24x² − 20x − 24
Hint: Multiply every term inside the brackets by −4: −24x² − 20x − 24.
Question 6
Divide: (−15x² − 25x + 25) ÷ 5
- −15x² − 25x + 5
- −3x² − 5x + 4
- −3x² − 5x − 3
- −3x² − 25x + 25
- −3x² − 5x + 5
−3x² − 5x + 5
Hint: Divide every term by 5: 25, -25, -15 ÷ 5. The result is −3x² − 5x + 5.