Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline6n3+6n2+7n+76n^3 + 6n^2 + 7n + 7

Full solution

Q. Factor.\newline6n3+6n2+7n+76n^3 + 6n^2 + 7n + 7
  1. Factor Common Terms: Look for common factors in the first two terms and the last two terms separately.\newlineWe can factor out 6n26n^2 from the first two terms, and we can factor out 77 from the last two terms.\newline6n3+6n2+7n+7=6n2(n+1)+7(n+1)6n^3 + 6n^2 + 7n + 7 = 6n^2(n + 1) + 7(n + 1)
  2. Factor Out Common Factors: Check if there is a common binomial factor from the two groups.\newlineBoth groups have a common factor of (n+1)(n + 1).\newline6n2(n+1)+7(n+1)=(6n2+7)(n+1)6n^2(n + 1) + 7(n + 1) = (6n^2 + 7)(n + 1)
  3. Check for Common Binomial Factor: Write the final factored form of the polynomial.\newlineThe factored form of 6n3+6n2+7n+76n^3 + 6n^2 + 7n + 7 is (6n2+7)(n+1)(6n^2 + 7)(n + 1).