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9th grade · Math · Unit 14 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.

California 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

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 + 14x + 48.

    • (x + 8)(x + 6)
    • (x + 14)(x + 1)
    • (x + 8)(x − 6)
    • (x − 8)(x − 6)

  2. Question 2

    Factor x² − 9.

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

  3. Question 3

    Solve x² = 144.

    • x = 12
    • x = 144 or x = −144
    • x = 12 or x = −12
    • x = 72

  4. Question 4

    Factor 24x − 12 completely.

    • 6x(4x − 2)
    • 6(24x − 2)
    • 6(4x − 2)
    • 24(x − 2)

  5. Question 5

    Solve (x − 9)(x + 1) = 0.

    • x = −9
    • x = 8
    • x = −1 or x = 9
    • x = −9 or x = 1

  6. Question 6

    Solve 3x² = 243.

    • x = 9
    • x = 121.5
    • x = 81 or x = −81
    • x = 9 or x = −9

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