Using the GCF, what is the factored form of 24v – 84? 3(8v – 28) 24(v – 60) 12(2v – 7) 6(4v – 14)

Mathematics

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Step-by-step solution

2 steps

The factored form of 24v−8424v - 84 using the GCF is 12(2v−7)12(2v - 7).

  1. Find the GCF of the coefficients.

    The coefficients are 24 and 84.
    Prime factorization of 24: 23×3=2×2×2×32^3 \times 3 = 2 \times 2 \times 2 \times 3
    Prime factorization of 84: 22×3×7=2×2×3×72^2 \times 3 \times 7 = 2 \times 2 \times 3 \times 7
    The greatest common factor (GCF) is the product of the common prime factors raised to the lowest power: 22×3=4×3=122^2 \times 3 = 4 \times 3 = 12.

  2. Factor out the GCF from the expression.

    Divide each term in the expression by the GCF:
    24v÷12=2v24v \div 12 = 2v
    84÷12=784 \div 12 = 7
    So, the factored form is 12(2v−7)12(2v - 7).

    The final answer is 12(2v−7)\boxed{12(2v - 7)}.

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