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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.

Minnesota K-12 Academic Standards benchmark: 9.3.6.4; 9.3.6.5 · factoring quadratics 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 Minnesota

In the Minnesota K-12 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: Minnesota Department of Education (MDE)

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 − 16.

    • (x + 4)(x + 4)
    • (x − 4)(x − 4)
    • (x − 4)(x + 4)
    • (x − 16)(x + 1)

  2. Question 2

    Solve (x − 8)(x + 8) = 0.

    • x = 0
    • x = −64
    • x = −8 or x = 8

  3. Question 3

    Solve x² = 64.

    • x = 8 or x = −8
    • x = 64 or x = −64
    • x = 8
    • x = 32

  4. Question 4

    Factor 15x + 21 completely.

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

  5. Question 5

    Factor x² − 16x + 63.

    • (x + 9)(x + 7)
    • (x − 16)(x + 1)
    • (x − 9)(x + 7)
    • (x − 9)(x − 7)

  6. Question 6

    Factor x² − 4.

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

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