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Polynomial Factoring Methods Flashcards

7 cards from real IBEW practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Polynomial Factoring Methods flashcards as text

  1. Factor: x³ + 8

    Answer: (x + 2)(x² - 2x + 4)

    Sum of cubes: x³ + 2³ = (x + 2)(x² − 2x + 4) using a³ + b³ = (a + b)(a² − ab + b²).

  2. Factor: 4x² + 12x + 9

    Answer: (2x + 3)²

    4x² + 12x + 9 = (2x)² + 2(2x)(3) + 3² = (2x + 3)², a perfect square trinomial.

  3. Which is the fully factored form of 2x³ - 8x?

    Answer: 2x(x - 2)(x + 2)

    Factor out 2x: 2x(x² − 4), then factor the difference of squares: 2x(x − 2)(x + 2).

  4. Factor: 3x² + 10x - 8

    Answer: (3x - 2)(x + 4)

    AC method: 3×(−8)=−24; factors summing to 10 are 12 and −2; grouping gives (3x − 2)(x + 4).

  5. What technique is most efficient for factoring x⁶ - 64?

    Answer: Difference of squares applied twice

    x⁶ − 64 = (x³)² − 8² = (x³ − 8)(x³ + 8), then each cubic can be factored further.

  6. Factor: x² - 2x - 48

    Answer: (x - 8)(x + 6)

    Find factors of −48 adding to −2: −8 and 6, giving (x − 8)(x + 6).

  7. After factoring out the GCF from 15x²y - 10xy², what remains inside the parentheses?

    Answer: 3x - 2y

    GCF of 15x²y and 10xy² is 5xy; dividing each term gives 3x − 2y inside the parentheses.