Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline18x3+10x2+9x+518x^3 + 10x^2 + 9x + 5

Full solution

Q. Factor.\newline18x3+10x2+9x+518x^3 + 10x^2 + 9x + 5
  1. Identify Grouping Method: Step Title: Identify the Grouping Method\newlineConcise Step Description: Since the expression is a cubic polynomial, we will use the grouping method to factor by grouping the terms into pairs.\newlineStep Calculation: Group the terms as (18x3+10x2)(18x^3 + 10x^2) and (9x+5)(9x + 5).\newlineStep Output: Grouped terms: (18x3+10x2)+(9x+5)(18x^3 + 10x^2) + (9x + 5)
  2. Factor by Grouping: Step Title: Factor by Grouping\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: From the first group 18x3+10x218x^3 + 10x^2, the greatest common factor is 2x22x^2, resulting in 2x2(9x+5)2x^2(9x + 5). From the second group (9x+5)(9x + 5), the greatest common factor is 11, so it remains (9x+5)(9x + 5).\newlineStep Output: Factored groups: 2x2(9x+5)+1(9x+5)2x^2(9x + 5) + 1(9x + 5)
  3. Factor Out Common Binomial: Step Title: Factor Out the Common Binomial\newlineConcise Step Description: Factor out the common binomial factor from the factored groups.\newlineStep Calculation: The common binomial factor is (9x+5)(9x + 5), so we factor it out from both terms.\newlineStep Output: Factored form: (9x+5)(2x2+1)(9x + 5)(2x^2 + 1)