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Factor.\newline5t2+25t+305t^2 + 25t + 30

Full solution

Q. Factor.\newline5t2+25t+305t^2 + 25t + 30
  1. Identify GCF: First, let's look for a greatest common factor (GCF) that we can pull out from all the terms.\newlineGCF of 5t25t^2, 25t25t, and 3030 is 55.\newlineSo, we take out 55 and rewrite the expression.\newline5(t2+5t+6)5(t^2 + 5t + 6)
  2. Factor Out GCF: Now, we need to factor the quadratic inside the parentheses.\newlineWe're looking for two numbers that multiply to 66 (the constant term) and add up to 55 (the coefficient of tt).\newlineThose numbers are 22 and 33.
  3. Factor Quadratic: So, we can write t2+5t+6t^2 + 5t + 6 as (t+2)(t+3)(t + 2)(t + 3). Now, we bring back the 55 we factored out earlier. 5(t+2)(t+3)5(t + 2)(t + 3)
  4. Correct Mistake: Oops, I made a mistake. The correct numbers that multiply to 66 and add up to 55 are 22 and 33, but I forgot to include the GCF in the factored form.\newlineThe correct factored form should be 5(t+2)(t+3)5(t + 2)(t + 3).