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9th grade · Math · Unit 12 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.8(A); A.10(E); A.10(F) · factoring trinomials and differences of squares, 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 12 of 16 in 9th grade Math, after Expressions and before Exponents & Powers.

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: Texas Education Agency (TEA)

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 3x − 18 completely.

    • 3(x − 6)
    • 3x(x − 6)
    • 3(3x − 6)

  2. Question 2

    Factor x² − 4.

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

  3. Question 3

    Solve (x − 7)(x + 6) = 0.

    • x = 1
    • x = −6 or x = 7
    • x = −7 or x = 6
    • x = −42

  4. Question 4

    Solve 2x² = 162.

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

  5. Question 5

    Factor x² + 4x + 3.

    • (x + 4)(x + 1)
    • (x + 1)(x + 3)
    • (x + 1)(x − 3)
    • (x − 1)(x − 3)

  6. Question 6

    Solve 3x² = 48.

    • x = 16 or x = −16
    • x = 24
    • x = 4
    • x = 4 or x = −4

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