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Factor.\newline20z3+10z2+18z+920z^3 + 10z^2 + 18z + 9

Full solution

Q. Factor.\newline20z3+10z2+18z+920z^3 + 10z^2 + 18z + 9
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 20z320z^3 and 10z210z^2, the common factor is 10z210z^2.\newlineFor the last two terms, 18z18z and 99, the common factor is 99.
  2. Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms.\newlineFactor out 10z210z^2 from 20z3+10z220z^3 + 10z^2 to get 10z2(2z+1)10z^2(2z + 1).\newlineFactor out 99 from 18z+918z + 9 to get 9(2z+1)9(2z + 1).
  3. Write New Expression: Write down the new expression using the factored terms.\newlineThe new expression is 10z2(2z+1)+9(2z+1)10z^2(2z + 1) + 9(2z + 1).
  4. Factor Out Binomial Factor: Factor out the common binomial factor (2z+1)(2z + 1) from the two terms.\newlineThe factored form is (2z+1)(10z2+9)(2z + 1)(10z^2 + 9).