Factor. 3t^3 + 6t^2 + 7t + 14 ______

Identify Common Factors: Look for common factors in each pair of terms. We can pair the terms as (3t^3 + 6t^2) and (7t + 14) to look for common factors.Factor First Pair: Factor out the common factor from the first pair of terms. The common factor in 3t^3 and 6t^2 is 3t^2. 3t^3 + 6t^2 = 3t^2(t + 2)Factor Second Pair: Factor out the common factor from the second pair of terms. The common factor in 7t and 14 is 7. 7t + 14 = 7(t + 2)Write Down Findings: Write down what we have found so far. We have: 3t^3 + 6t^2 = 3t^2(t + 2) 7t + 14 = 7(t + 2) Now, we can see that (t + 2) is a common factor.Factor Out Common Factor: Factor out the common factor (t + 2) from the entire expression. We can write the original expression as: 3t^3 + 6t^2 + 7t + 14 = 3t^2(t + 2) + 7(t + 2) Now, factor out (t + 2): 3t^3 + 6t^2 + 7t + 14 = (t + 2)(3t^2 + 7)

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Factor. $\newline$ $3t^3 + 6t^2 + 7t + 14$

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Q. Factor.

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3t^3 + 6t^2 + 7t + 14

Identify Common Factors: Look for common factors in each pair of terms. $\newline$ We can pair the terms as $(3t^3 + 6t^2)$ and $(7t + 14)$ to look for common factors.
Factor First Pair: Factor out the common factor from the first pair of terms. $\newline$ The common factor in $3t^3$ and $6t^2$ is $3t^2$ . $\newline$ $3t^3 + 6t^2 = 3t^2(t + 2)$
Factor Second Pair: Factor out the common factor from the second pair of terms. $\newline$ The common factor in $7t$ and $14$ is $7$ . $\newline$ $7t + 14 = 7(t + 2)$
Write Down Findings: Write down what we have found so far. $\newline$ We have: $\newline$ $3t^3 + 6t^2 = 3t^2(t + 2)$ $\newline$ $7t + 14 = 7(t + 2)$ $\newline$ Now, we can see that $(t + 2)$ is a common factor.
Factor Out Common Factor: Factor out the common factor $(t + 2)$ from the entire expression. $\newline$ We can write the original expression as: $\newline$ $3t^3 + 6t^2 + 7t + 14 = 3t^2(t + 2) + 7(t + 2)$ $\newline$ Now, factor out $(t + 2)$ : $\newline$ $3t^3 + 6t^2 + 7t + 14 = (t + 2)(3t^2 + 7)$