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9th grade · Math · Unit 14 of 17

Factoring & Quadratics

Factor and solve x² equations

What your child practices

Factoring quadratic expressions (common factors, trinomials, difference of squares) and solving quadratic equations by factoring and square roots.

Arizona Academic Standards learning standard: A1.A-REI.B.4; A1.A-SSE.B.3; A1.A-SSE.A.2 · factoring quadratic expressions and solving quadratic equations by factoring and taking square roots

How we explain it

Children can open this short lesson before they practice.

  1. To factor x² + bx + c, find two numbers that multiply to c and add to b.
  2. If a product is 0, one of the factors is 0.
  3. x² = k has two answers: √k and −√k.

Example: Solve x² + 5x + 6 = 0. 2 × 3 = 6 and 2 + 3 = 5: (x + 2)(x + 3) = 0. x + 2 = 0 or x + 3 = 0. Answer: x = −2 or x = −3

Factoring & Quadratics in Arizona

In the Arizona Academic Standards, this is unit 14 of 17 in 9th grade Math, after Linear or Exponential? and before Rearranging Formulas.

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.

  1. Question 1

    Factor x² + 2x − 8.

    • (x + 2)(x + 1)
    • (x − 2)(x + 4)
    • (x + 2)(x − 4)
    • (x − 2)(x − 4)

  2. Question 2

    Solve 2x² = 50.

    • x = 5 or x = −5
    • x = 5
    • x = 25
    • x = 25 or x = −25

  3. Question 3

    Solve (x − 7)(x + 7) = 0.

    • x = −49
    • x = −7 or x = 7
    • x = 0

  4. Question 4

    Factor x² − 121.

    • (x − 121)(x + 1)
    • (x + 11)(x + 11)
    • (x − 11)(x − 11)
    • (x − 11)(x + 11)

  5. Question 5

    Factor 24x − 12 completely.

    • 6(24x − 2)
    • 6(4x − 2)
    • 24(x − 2)
    • 6x(4x − 2)

  6. Question 6

    Factor 6x + 15 completely.

    • 3(6x + 5)
    • 3(2x + 5)
    • 6(x + 5)
    • 3x(2x + 5)

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