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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: 4x² - 25

    Answer: (2x - 5)(2x + 5)

    4x² − 25 is a difference of squares: (2x)² − 5² = (2x − 5)(2x + 5).

  2. What is the GCF of 12x³, 18x², and 6x?

    Answer: 6x

    The GCF of 12, 18, and 6 is 6, and the lowest power of x is x¹, so GCF = 6x.

  3. Factor completely: x⁴ - 16

    Answer: (x - 2)(x + 2)(x² + 4)

    x⁴ − 16 = (x² − 4)(x² + 4) = (x − 2)(x + 2)(x² + 4); x² + 4 cannot be factored further over integers.

  4. Factor: x² - x - 12

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

    Find numbers multiplying to −12 and adding to −1: −4 and 3, giving (x − 4)(x + 3).

  5. If one factor of x² - 7x + 10 is (x - 2), what is the other factor?

    Answer: (x - 5)

    Dividing x² − 7x + 10 by (x − 2) gives (x − 5), verified by −2 × −5 = 10 and −2 + −5 = −7.

  6. Factor: 6x² - 7x - 3

    Answer: (3x + 1)(2x - 3)

    AC method: 6×(−3)=−18; factors summing to −7 are −9 and 2; rewrite and group to get (3x + 1)(2x − 3).

  7. Factor: x² + 4x - 21

    Answer: (x + 7)(x - 3)

    Find factors of −21 adding to 4: 7 and −3, giving (x + 7)(x − 3).