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Polynomials and Factoring Flashcards

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

Read the first 6 Polynomials and Factoring flashcards as text

  1. Multiply: (x - 4)(x + 4).

    Answer: x² - 16

    This is a difference of squares: (a - b)(a + b) = a² - b² = x² - 16.

  2. Factor: x² - 9.

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

    x² - 9 = x² - 3² is a difference of squares, factoring as (x + 3)(x - 3).

  3. Subtract: (4x² - 3x + 2) - (x² + 2x - 5).

    Answer: 3x² - 5x + 7

    Distribute the negative: 4x² - 3x + 2 - x² - 2x + 5 = 3x² - 5x + 7.

  4. What is the leading coefficient of -3x⁴ + 2x² - x?

    Answer: -3

    The leading coefficient is the coefficient of the highest-degree term, which is -3.

  5. Factor: 2x² - 8x.

    Answer: 2x(x - 4)

    Factor out 2x: 2x(x - 4).

  6. Which is the correct expansion of (x + 5)(x - 3)?

    Answer: x² + 2x - 15

    FOIL: x² - 3x + 5x - 15 = x² + 2x - 15.