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Polynomials and Factoring Flashcards

6 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 completely: x² - 9

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

    This is a difference of squares: a² - b² = (a+b)(a-b). x² - 9 = x² - 3² = (x+3)(x-3).

  2. Multiply: (2x + 3)(x - 4)

    Answer: 2x² - 5x - 12

    FOIL: 2x·x + 2x·(-4) + 3·x + 3·(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.

  3. Factor: x² + 7x + 12

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

    Find two numbers that multiply to 12 and add to 7: 3 and 4. So (x+3)(x+4).

  4. What is the GCF of 12x³y², 18x²y, and 24xy³?

    Answer: 6xy

    GCF of 12, 18, 24 is 6. Lowest power of x is x¹. Lowest power of y is y¹. GCF = 6xy.

  5. Factor completely: 3x² - 12

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

    Factor out 3: 3(x² - 4). Then factor difference of squares: 3(x+2)(x-2).

  6. Simplify: (3x²y)(4xy³)

    Answer: 12x³y⁴

    Multiply coefficients: 3×4=12. Add exponents: x²·x¹=x³, y¹·y³=y⁴. Result: 12x³y⁴.