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Factor.\newline8v3+6v220v158v^3 + 6v^2 - 20v - 15

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Q. Factor.\newline8v3+6v220v158v^3 + 6v^2 - 20v - 15
  1. Identify Common Factors: Look for common factors in pairs of terms.\newlineWe can group the terms as follows: 8v3+6v28v^3 + 6v^2 and 20v15 -20v - 15.\newlineNow, factor out the greatest common factor from each group.\newlineFor the first group, the greatest common factor is 2v22v^2.\newlineFor the second group, the greatest common factor is 5 -5.
  2. Factor Out Common Factors: Factor out the common factors from each group.\newline8v3+6v2=2v2(4v+3)8v^3 + 6v^2 = 2v^2(4v + 3)\newline20v15=5(4v+3)-20v - 15 = -5(4v + 3)\newlineNow we have: 2v2(4v+3)5(4v+3)2v^2(4v + 3) - 5(4v + 3)
  3. Factor Out Common Binomial: Factor out the common binomial factor.\newlineBoth groups contain the common binomial factor (4v+3)(4v + 3).\newlineFactor out (4v+3)(4v + 3) from the expression.\newlineThe factored form is: (2v25)(4v+3)(2v^2 - 5)(4v + 3)