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Factor 24 k+36 q-12 to identify the equivalent expressions. Choose 2 answers: A 12(2k+3q-1) B 3(8k+12 q-4) c 6(3k+6q-12) D 12(2k+3q)

Factor 24k+36q−12 24 k+36 q-12 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 12(2k+3q−1) 12(2 k+3 q-1) \newlineB 3(8k+12q−4) 3(8 k+12 q-4) \newlinec 6(3k+6q−12) 6(3 k+6 q-12) \newlineD 12(2k+3q) 12(2 k+3 q)

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Full solution

Q. Factor 24k+36q−12 24 k+36 q-12 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 12(2k+3q−1) 12(2 k+3 q-1) \newlineB 3(8k+12q−4) 3(8 k+12 q-4) \newlinec 6(3k+6q−12) 6(3 k+6 q-12) \newlineD 12(2k+3q) 12(2 k+3 q)
  1. Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression 24k+36q−1224k + 36q - 12. The GCF of 2424, 3636, and 1212 is 1212.
  2. Factor Out GCF: Factor out the GCF from each term in the expression. \newline24k+36q−12=12(2k)+12(3q)−12(1)24k + 36q - 12 = 12(2k) + 12(3q) - 12(1)
  3. Simplify Factored Expression: Simplify the factored expression by combining the terms inside the parentheses. 24k+36q−12=12(2k+3q−1)24k + 36q - 12 = 12(2k + 3q - 1)
  4. Check Answer Choices: Check the answer choices to see which ones are equivalent to the simplified expression.\newlineThe correct factored expression is 12(2k+3q−1)12(2k + 3q - 1), so option AA is correct.
  5. Check Other Choices: Check the other answer choices for equivalence by simplifying them if necessary.\newlineOption B: 3(8k+12q−4)=3(8k)+3(12q)−3(4)=24k+36q−123(8k + 12q - 4) = 3(8k) + 3(12q) - 3(4) = 24k + 36q - 12, which is the original expression, so option B is also correct.\newlineOption C: 6(3k+6q−12)6(3k + 6q - 12) simplifies to 6(3k)+6(6q)−6(12)=18k+36q−726(3k) + 6(6q) - 6(12) = 18k + 36q - 72, which is not equivalent to the original expression.\newlineOption D: 12(2k+3q)12(2k + 3q) simplifies to 12(2k)+12(3q)=24k+36q12(2k) + 12(3q) = 24k + 36q, which lacks the −12-12 term from the original expression, so it is not equivalent.

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