Factor. 7v^3 + 7v^2 + 2v + 2 ______

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. We can factor out 7v^2 from the first two terms, 7v^3 and 7v^2. 7v^3 + 7v^2 = 7v^2(v + 1) We can factor out 2 from the last two terms, 2v and 2. 2v + 2 = 2(v + 1)Write Factored Groups: Write the expression with the factored groups. Now we have: 7v^2(v + 1) + 2(v + 1) Notice that (v + 1) is a common factor.Factor Out Common Factor: Factor out the common factor (v + 1). We can now factor (v + 1) out of the expression: 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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Q. Factor.

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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.