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Factor.\newline4n316n2+3n124n^3 - 16n^2 + 3n - 12

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Q. Factor.\newline4n316n2+3n124n^3 - 16n^2 + 3n - 12
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 4n34n^3 and 16n2-16n^2, the common factor is 4n24n^2.\newlineFor the last two terms, 3n3n and 12-12, the common factor is 33.
  2. Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms.\newline4n316n2=4n2(n4)4n^3 - 16n^2 = 4n^2(n - 4)\newline3n12=3(n4)3n - 12 = 3(n - 4)
  3. Write Factored Expression: Write the expression with the factored terms. 4n316n2+3n12=4n2(n4)+3(n4)4n^3 - 16n^2 + 3n - 12 = 4n^2(n - 4) + 3(n - 4)
  4. Factor Out Binomial Factor: Factor out the common binomial factor (n4)(n - 4).4n2(n4)+3(n4)=(4n2+3)(n4)4n^2(n - 4) + 3(n - 4) = (4n^2 + 3)(n - 4)