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Factor.\newline6s3+6s2+7s+76s^3 + 6s^2 + 7s + 7

Full solution

Q. Factor.\newline6s3+6s2+7s+76s^3 + 6s^2 + 7s + 7
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 6s36s^3 and 6s26s^2, the common factor is 6s26s^2.\newlineFor the last two terms, 7s7s and 77, the common factor is 77.
  2. Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms.\newline6s3+6s26s^3 + 6s^2 can be factored as 6s2(s+1)6s^2(s + 1).\newline7s+77s + 7 can be factored as 7(s+1)7(s + 1).
  3. Combine Factored Expressions: Now, we have the expression in the form of 6s2(s+1)+7(s+1)6s^2(s + 1) + 7(s + 1). Notice that (s+1)(s + 1) is a common factor.
  4. Final Factored Form: Factor out the common factor (s+1)(s + 1) from the entire expression.\newlineThe factored form of the polynomial is (s+1)(6s2+7)(s + 1)(6s^2 + 7).