Question

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Explanation:

Problem 1: \( 5v^3 + 30v^2 - 8v - 48 \)

Step 1: Group terms

Group the first two terms and the last two terms:
\( (5v^3 + 30v^2) + (-8v - 48) \)

Step 2: Factor out GCF from each group

Factor \( 5v^2 \) from the first group and \( -8 \) from the second group:
\( 5v^2(v + 6) - 8(v + 6) \)

Step 3: Factor out common binomial

Factor out \( (v + 6) \) from both terms:
\( (5v^2 - 8)(v + 6) \)

Step 1: Group terms

Group the first two terms and the last two terms:
\( (15x^3 - 24x^2) + (10x - 16) \)

Step 2: Factor out GCF from each group

Factor \( 3x^2 \) from the first group and \( 2 \) from the second group:
\( 3x^2(5x - 8) + 2(5x - 8) \)

Step 3: Factor out common binomial

Factor out \( (5x - 8) \) from both terms:
\( (3x^2 + 2)(5x - 8) \)

Step 1: Group terms

Group the first two terms and the last two terms:
\( (12a^3 - 3a^2) + (28a - 7) \)

Step 2: Factor out GCF from each group

Factor \( 3a^2 \) from the first group and \( 7 \) from the second group:
\( 3a^2(4a - 1) + 7(4a - 1) \)

Step 3: Factor out common binomial

Factor out \( (4a - 1) \) from both terms:
\( (3a^2 + 7)(4a - 1) \)

Answer:

\( (5v^2 - 8)(v + 6) \)

Problem 2: \( 15x^3 - 24x^2 + 10x - 16 \)