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Grade 9 · Math · Unit 3 of 8

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.

BC Curriculum learning standard: Operations with polynomials of degree 2 or less: add, subtract, multiply and divide by a constant

How we explain it

Children can open this short lesson before they practise.

  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

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 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.

  2. Question 2

    What is the degree of 7x − 3?

    answer box

    Show answer

    1

    Hint: The degree is the highest exponent on the variable.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

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