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Factor. $\newline$ $7v^3 + 7v^2 + 2v + 2$

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Factor by grouping

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Q. Factor.

\newline

7v^3 + 7v^2 + 2v + 2

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. $\newline$ We can factor out $7v^2$ from the first two terms, $7v^3$ and $7v^2$ . $\newline$ $7v^3 + 7v^2 = 7v^2(v + 1)$ $\newline$ We can factor out $2$ from the last two terms, $2v$ and $2$ . $\newline$ $2v + 2 = 2(v + 1)$
Write Factored Groups: Write the expression with the factored groups. $\newline$ Now we have: $\newline$ $7v^2(v + 1) + 2(v + 1)$ $\newline$ Notice that $(v + 1)$ is a common factor.
Factor Out Common Factor: Factor out the common factor $(v + 1)$ . $\newline$ We can now factor $(v + 1)$ out of the expression: $\newline$ $7v^2(v + 1) + 2(v + 1) = (v + 1)(7v^2 + 2)$
Check Quadratic Factorability: Check if the remaining quadratic can be factored further. The quadratic $7v^2 + 2$ does not have any common factors and cannot be factored further over the integers.

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