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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.

Alaska content standards learning standard: A-REI.4; A-SSE.3; A-SSE.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 Alaska

In the Alaska content 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: Alaska Department of Education and Early Development

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 4x − 20 completely.

    • 4(x − 5)
    • 4x(x − 5)
    • 4(4x − 5)

  2. Question 2

    Factor x² − 144.

    • (x − 12)(x + 12)
    • (x + 12)(x + 12)
    • (x − 144)(x + 1)
    • (x − 12)(x − 12)

  3. Question 3

    Solve 2x² = 98.

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

  4. Question 4

    Factor x² + 5x + 4.

    • (x + 5)(x + 1)
    • (x + 4)(x − 1)
    • (x − 4)(x − 1)
    • (x + 4)(x + 1)

  5. Question 5

    Solve (x + 7)(x − 1) = 0.

    • x = −7 or x = 1
    • x = −7
    • x = −6
    • x = −1 or x = 7

  6. Question 6

    Solve (x − 4)(x + 7) = 0.

    • x = −7 or x = 4
    • x = −4 or x = 7
    • x = −28
    • x = −3

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