Factor. 9t^3 + 9t^2 + t + 1 ______

Identify Common Factors: Look for common factors in each pair of terms. We can pair the terms as (9t^3 + 9t^2) and (t + 1) to look for common factors.Factor First Pair: Factor out the common factor from the first pair of terms. The common factor in 9t^3 and 9t^2 is 9t^2. So, 9t^3 + 9t^2 can be factored as 9t^2(t + 1).Factor Second Pair: Factor out the common factor from the second pair of terms. The second pair of terms is t + 1, which does not have a common factor other than 1. So, t + 1 remains as it is.Combine Factored Forms: Combine the factored forms from Step 2 and Step 3. We have 9t^2(t + 1) from the first pair and t + 1 from the second pair. Since t + 1 is a common factor, we can factor it out. The factored form of 9t^3 + 9t^2 + t + 1 is (t + 1)(9t^2 + 1).

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9t^3 + 9t^2 + t + 1

Identify Common Factors: Look for common factors in each pair of terms. $\newline$ We can pair the terms as $9t^3 + 9t^2$ and $t + 1$ to look for common factors.
Factor First Pair: Factor out the common factor from the first pair of terms. $\newline$ The common factor in $9t^3$ and $9t^2$ is $9t^2$ . $\newline$ So, $9t^3 + 9t^2$ can be factored as $9t^2(t + 1)$ .
Factor Second Pair: Factor out the common factor from the second pair of terms. $\newline$ The second pair of terms is $t + 1$ , which does not have a common factor other than $1$ . $\newline$ So, $t + 1$ remains as it is.
Combine Factored Forms: Combine the factored forms from Step $2$ and Step $3$ . $\newline$ We have $9t^2(t + 1)$ from the first pair and $t + 1$ from the second pair. $\newline$ Since $t + 1$ is a common factor, we can factor it out. $\newline$ The factored form of $9t^3 + 9t^2 + t + 1$ is $(t + 1)(9t^2 + 1)$ .