Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline6x3+12x2x26x^3 + 12x^2 - x - 2

Full solution

Q. Factor.\newline6x3+12x2x26x^3 + 12x^2 - x - 2
  1. Group Terms: Group the terms to find common factors.\newlineWe can group the terms as follows: (6x3+12x2)(6x^3 + 12x^2) and (x2)(-x - 2).
  2. Factor Common Factors: Factor out the greatest common factor from each group.\newlineFrom the first group 6x3+12x26x^3 + 12x^2, we can factor out 6x26x^2, which gives us 6x2(x+2)6x^2(x + 2).\newlineFrom the second group x2-x - 2, we can factor out 1-1, which gives us 1(x+2)-1(x + 2).
  3. Write Factored Expression: Write the expression with the factored groups.\newlineNow we have 6x2(x+2)1(x+2)6x^2(x + 2) - 1(x + 2).
  4. Factor Common Binomial: Factor out the common binomial factor.\newlineWe can see that (x+2)(x + 2) is a common factor in both terms, so we factor it out to get (x+2)(6x21)(x + 2)(6x^2 - 1).
  5. Check Quadratic Factorization: Check if the remaining quadratic can be factored further. The quadratic 6x216x^2 - 1 is a difference of squares, which can be factored as (6x1)(6x+1)(\sqrt{6}x - 1)(\sqrt{6}x + 1).
  6. Write Final Form: Write the final factored form.\newlineThe final factored form of the polynomial is (x+2)(6x1)(6x+1)(x + 2)(\sqrt{6}x - 1)(\sqrt{6}x + 1).