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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.

Maine Learning Results learning standard: HSA.REI.B.4; HSA.SSE.B.3; HSA.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 Maine

In the Maine Learning Results, 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: Maine 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

    Solve x² = 81.

    • x = 9
    • x = 81 or x = −81
    • x = 9 or x = −9
    • x = 40.5

  2. Question 2

    Factor x² − 121.

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

  3. Question 3

    Factor x² − 8x + 7.

    • (x − 1)(x − 7)
    • (x − 8)(x + 1)
    • (x + 1)(x + 7)
    • (x − 1)(x + 7)

  4. Question 4

    Solve (x + 6)(x + 8) = 0.

    • x = 6 or x = 8
    • x = 48
    • x = −14
    • x = −8 or x = −6

  5. Question 5

    Factor 18x + 30 completely.

    • 6x(3x + 5)
    • 18(x + 5)
    • 6(3x + 5)
    • 6(18x + 5)

  6. Question 6

    Factor 16x + 28 completely.

    • 4x(4x + 7)
    • 16(x + 7)
    • 4(16x + 7)
    • 4(4x + 7)

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