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Factor.\newline3x35x2+12x203x^3 - 5x^2 + 12x - 20

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Q. Factor.\newline3x35x2+12x203x^3 - 5x^2 + 12x - 20
  1. Identify Common Factor: Look for a common factor in all terms.\newlineCheck if there is a greatest common factor (GCF) that can be factored out from all terms of the polynomial 3x35x2+12x203x^3 - 5x^2 + 12x - 20.\newlineThe terms do not share a common factor other than 11.
  2. Group Terms: Group terms to facilitate factoring by grouping.\newlineGroup the terms into two pairs: (3x35x2)(3x^3 - 5x^2) and (12x20)(12x - 20).
  3. Factor Out GCF: Factor out the GCF from each group.\newlineFrom the first group 3x35x23x^3 - 5x^2, factor out x2x^2, which gives x2(3x5)x^2(3x - 5).\newlineFrom the second group 12x2012x - 20, factor out 44, which gives 4(3x5)4(3x - 5).
  4. Write Factored Form: Write the factored form of the polynomial.\newlineBoth groups now have a common factor of (3x5)(3x - 5).\newlineFactor out (3x5)(3x - 5) from x2(3x5)+4(3x5)x^2(3x - 5) + 4(3x - 5).\newlineThe factored form is (3x5)(x2+4)(3x - 5)(x^2 + 4).