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Factor.\newline20y310y2+6y320y^3 - 10y^2 + 6y - 3

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Q. Factor.\newline20y310y2+6y320y^3 - 10y^2 + 6y - 3
  1. Identify Common Factors: Look for common factors in each pair of terms. We can pair the first two terms and the last two terms to look for common factors.
  2. Factor First Pair: Factor out the greatest common factor from the first pair of terms.\newlineThe greatest common factor of 20y320y^3 and 10y210y^2 is 10y210y^2.\newline20y310y2=10y2(2y1)20y^3 - 10y^2 = 10y^2(2y - 1)
  3. Factor Second Pair: Factor out the greatest common factor from the second pair of terms.\newlineThe greatest common factor of 6y6y and 3-3 is 33.\newline6y3=3(2y1)6y - 3 = 3(2y - 1)
  4. Write Factored Expression: Write the expression with the factored pairs.\newline20y310y2+6y3=10y2(2y1)+3(2y1)20y^3 - 10y^2 + 6y - 3 = 10y^2(2y - 1) + 3(2y - 1)
  5. Factor Common Binomial: Factor out the common binomial factor.\newlineBoth terms have a common factor of (2y1)(2y - 1).\newline20y310y2+6y3=(10y2+3)(2y1)20y^3 - 10y^2 + 6y - 3 = (10y^2 + 3)(2y - 1)