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9th grade · Math · Unit 14 of 22

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.

New York State Learning Standards learning standard: AI-A.REI.4; AI-A.SSE.3; AI-A.APR.3 · factoring quadratic expressions, finding zeros, and solving quadratic equations by factoring and 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 New York

In the New York State Learning Standards, this is unit 14 of 22 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: New York State Education Department (NYSED)

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 − 5x − 6.

    • (x − 5)(x + 1)
    • (x + 6)(x − 1)
    • (x − 6)(x − 1)
    • (x − 6)(x + 1)

  2. Question 2

    Solve (x + 6)(x + 7) = 0.

    • x = −13
    • x = 6 or x = 7
    • x = −7 or x = −6
    • x = 42

  3. Question 3

    Solve 2x² = 200.

    • x = 10
    • x = 100 or x = −100
    • x = 10 or x = −10
    • x = 100

  4. Question 4

    Factor 9x + 15 completely.

    • 3(3x + 5)
    • 3x(3x + 5)
    • 3(9x + 5)
    • 9(x + 5)

  5. Question 5

    Factor x² − 49.

    • (x − 7)(x + 7)
    • (x − 49)(x + 1)
    • (x − 7)(x − 7)
    • (x + 7)(x + 7)

  6. Question 6

    Factor x² − 9.

    • (x − 3)(x + 3)
    • (x − 9)(x + 1)
    • (x − 3)(x − 3)
    • (x + 3)(x + 3)

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