Look for Common Factor: Step Title: Look for a Common FactorConcise Step Description: Check if there is a common factor in all terms of the polynomial.Step Calculation: The terms z3, −3z2, 5z, and −15 do not have a common factor other than 1.
Group Terms: Step Title: Group TermsConcise Step Description: Group terms to factor by grouping, which involves rearranging the terms into two binomials.Step Calculation: Group the terms as (z3−3z2)+(5z−15).
Factor Out Common Factor: Step Title: Factor Out the Greatest Common Factor from Each GroupConcise Step Description: Factor out the greatest common factor from each group.Step Calculation: Factor z2 out of the first group and 5 out of the second group to get z2(z−3)+5(z−3).
Factor Out Binomial Factor: Step Title: Factor Out the Common Binomial FactorConcise Step Description: Factor out the common binomial factor from the two groups.Step Calculation: Since both groups contain the factor (z−3), factor it out to get (z−3)(z2+5).