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.
Arizona Academic Standards learning standard: A1.A-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 Arizona
In the Arizona Academic Standards, 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: Arizona 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 6x² by its number of terms.
- quadrinomial
- binomial
- monomial
- trinomial
monomial
Hint: Count the terms: 6x² has 1. One term is a monomial, two a binomial, three a trinomial.
Question 2
What is the degree of −7x² − x + 9?
answer box
2
Hint: The degree is the highest exponent on the variable.
Question 3
Add: (9x² + 5x + 4) + (x² + 6)
- −12x² + 5x + 10
- 10x² + 5x + 10
- 10x² + 7x + 10
- 11x² + 5x + 10
- 9x² + 5x + 10
10x² + 5x + 10
Hint: Add the like terms: 9 + 1 = 10, 5 + 0 = 5, 4 + 6 = 10. The result is 10x² + 5x + 10.
Question 4
Subtract: (8x² − 3x − 8) − (3x² + 4x + 3)
- 4x² − 7x − 11
- 5x² + x − 5
- 11x² + x − 5
- 5x² − 7x − 11
- 5x² − 9x − 11
5x² − 7x − 11
Hint: Subtracting a polynomial changes the sign of every term in it: 8x² − 3x − 8 + (−3x² − 4x − 3). Then combine like terms to get 5x² − 7x − 11.
Question 5
Expand: 4(−4x² + 6x − 4)
- −16x² + 6x − 4
- −16x² + 24x − 4
- −16x² + 24x − 16
- −16x² + 24x − 15
- 10x
−16x² + 24x − 16
Hint: Multiply every term inside the brackets by 4: −16x² + 24x − 16.
Question 6
Divide: (−16x² + 24x + 12) ÷ 4
- −4x² + 24x + 12
- −16x² + 24x + 3
- −4x² + 6x − 1
- −4x² + 6x + 3
- 2x² + 6x + 3
−4x² + 6x + 3
Hint: Divide every term by 4: 12, 24, -16 ÷ 4. The result is −4x² + 6x + 3.