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9th grade · Math · Unit 2 of 22

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.

New York State Learning Standards learning standard: AI-A.APR.1 · adding, subtracting and multiplying polynomials

How we explain it

Children can open this short lesson before they practice.

  1. Like terms have the same variable and exponent. Only combine those.
  2. To add polynomials, combine like terms.
  3. 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 New York

In the New York State Learning Standards, this is unit 2 of 22 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: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Classify the polynomial 8x² by its number of terms.

    • binomial
    • monomial
    • quadrinomial
    • trinomial

  2. Question 2

    What is the degree of −7x?

    answer box

  3. Question 3

    Add: (x² + 4x − 4) + (x² + 8x + 4)

    • 2x² − 13x
    • 2x² + 11x
    • 2x² + 14x
    • 2x² + 12x
    • 4x² + 12x

  4. Question 4

    Subtract: (−2x² + 9) − (−2x² + 4x − 2)

    • −4x + 11
    • −4x + 12
    • −4x² + 4x + 7
    • −4x − 9
    • 4x + 7

  5. Question 5

    Expand: −6(6x² + 2x + 4)

    • −36x² + 2x + 4
    • −4x − 2
    • −36x² − 14x − 24
    • −36x² − 12x − 24
    • −36x² − 12x + 4

  6. Question 6

    Divide: (12x² − 2x + 10) ÷ 2

    • 6x² − x + 5
    • 12x² − 2x + 5
    • 6x² − 2x + 10
    • 6x² − x + 6
    • 6x² − x + 7

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