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Which expression is the result of factoring the expression below by taking out its greatest common factor? 8x^(2)-24=? Choose 1 answer: (A) 8x(x^(2)-3) (B) 8(x-3) (C) 8x(x-3) (D) 8(x^(2)-3)

Which expression is the result of factoring the expression below by taking out its greatest common factor?\newline8x2−24=8x^{2}-24=?\newlineChoose 11 answer:\newline(A) 8x(x2−3)8x(x^{2}-3)\newline(B) 8(x−3)8(x-3)\newline(C) 8x(x−3)8x(x-3)\newline(D) 8(x2−3)8(x^{2}-3)

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Full solution

Q. Which expression is the result of factoring the expression below by taking out its greatest common factor?\newline8x2−24=8x^{2}-24=?\newlineChoose 11 answer:\newline(A) 8x(x2−3)8x(x^{2}-3)\newline(B) 8(x−3)8(x-3)\newline(C) 8x(x−3)8x(x-3)\newline(D) 8(x2−3)8(x^{2}-3)
  1. Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression 8x2−248x^2 - 24.\newlineThe GCF of 8x28x^2 and 2424 is 88 since 88 is the largest number that divides both terms evenly.
  2. Factor out GCF from each term: Factor out the GCF from each term in the expression.\newlineThe expression 8x2−248x^2 - 24 can be factored as 8(x2)−8(3)8(x^2) - 8(3), which simplifies to 8(x2−3)8(x^2 - 3).
  3. Check factored expression: Check the factored expression to ensure that when the GCF is distributed back into the parentheses, the original expression is obtained.\newlineDistributing 88 back into the parentheses gives 8×x2−8×38 \times x^2 - 8 \times 3, which simplifies to 8x2−248x^2 - 24, the original expression.

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