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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.

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  1. Factor the sum of cubes: 8x³ + 27

    Answer: (2x + 3)(4x² - 6x + 9)

    Using a³ + b³ = (a + b)(a² − ab + b²) with a = 2x and b = 3: (2x + 3)(4x² − 6x + 9).

  2. Which polynomial CANNOT be factored over integers?

    Answer: x² + 9

    x² + 9 is a sum of squares, which cannot be factored over the integers.

  3. Factor by grouping: 2ax + 2ay + bx + by

    Answer: (2a + b)(x + y)

    Group as (2ax + 2ay) + (bx + by) = 2a(x + y) + b(x + y) = (2a + b)(x + y).

  4. What value of c makes x² + 8x + c a perfect square trinomial?

    Answer: 16

    For a perfect square, c = (8/2)² = 4² = 16, giving (x + 4)².

  5. Factor completely: 5x³ - 45x

    Answer: 5x(x - 3)(x + 3)

    Factor out 5x to get 5x(x² − 9), then factor the difference of squares: 5x(x − 3)(x + 3).

  6. Factor: 9x² - 30x + 25

    Answer: (3x - 5)²

    9x² − 30x + 25 = (3x)² − 2(3x)(5) + 5² = (3x − 5)², a perfect square trinomial.

  7. Factor: x² - 14x + 49

    Answer: (x - 7)²

    x² − 14x + 49 = (x − 7)² since 7² = 49 and 2(7) = 14.