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9th grade · Math · Unit 18 of 18

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.

Alabama Course of Study content standard: AIP.5; AIP.9 · factoring quadratic expressions and solving quadratic equations

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 Alabama

In the Alabama Course of Study, this is unit 18 of 18 in 9th grade Math, after Solving Systems.

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: Alabama State Department of Education (ALSDE)

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 (x + 4)(x − 6) = 0.

    • x = −24
    • x = 2
    • x = −4 or x = 6
    • x = −6 or x = 4

  2. Question 2

    Factor 15x + 35 completely.

    • 5x(3x + 7)
    • 15(x + 7)
    • 5(15x + 7)
    • 5(3x + 7)

  3. Question 3

    Solve 2x² = 98.

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

  4. Question 4

    Factor x² + 11x + 18.

    • (x + 11)(x + 1)
    • (x + 9)(x − 2)
    • (x + 9)(x + 2)
    • (x − 9)(x − 2)

  5. Question 5

    Factor x² − 81.

    • (x − 9)(x − 9)
    • (x − 9)(x + 9)
    • (x − 81)(x + 1)
    • (x + 9)(x + 9)

  6. Question 6

    Solve (x − 3)(x + 9) = 0.

    • x = −3 or x = 9
    • x = −27
    • x = −9 or x = 3
    • x = −6

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