Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newlinez33z2+5z15z^3 - 3z^2 + 5z - 15

Full solution

Q. Factor.\newlinez33z2+5z15z^3 - 3z^2 + 5z - 15
  1. Look for Common Factor: Step Title: Look for a Common Factor\newlineConcise Step Description: Check if there is a common factor in all terms of the polynomial.\newlineStep Calculation: The terms z3z^3, 3z2-3z^2, 5z5z, and 15-15 do not have a common factor other than 11.
  2. Group Terms: Step Title: Group Terms\newlineConcise Step Description: Group terms to factor by grouping, which involves rearranging the terms into two binomials.\newlineStep Calculation: Group the terms as (z33z2)+(5z15)(z^3 - 3z^2) + (5z - 15).
  3. Factor Out Common Factor: Step Title: Factor Out the Greatest Common Factor from Each Group\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: Factor z2z^2 out of the first group and 55 out of the second group to get z2(z3)+5(z3)z^2(z - 3) + 5(z - 3).
  4. Factor Out Binomial Factor: Step Title: Factor Out the Common Binomial Factor\newlineConcise Step Description: Factor out the common binomial factor from the two groups.\newlineStep Calculation: Since both groups contain the factor (z3)(z - 3), factor it out to get (z3)(z2+5)(z - 3)(z^2 + 5).