Factor. 2g^3 + g^2 + 14g + 7 ______

Identify Common Factors: Look for common factors in each pair of terms. We will first group the terms into pairs and look for common factors in each pair. Grouping: (2g^3 + g^2) and (14g + 7).Factor First Group: Factor out the common factor from the first group. In the first group (2g^3 + g^2), the common factor is g^2. Factoring out g^2 gives us g^2(2g + 1).Factor Second Group: Factor out the common factor from the second group. In the second group (14g + 7), the common factor is 7. Factoring out 7 gives us 7(2g + 1).Write Factored Expression: Write the factored form of the entire expression. We have found: 2g^3 + g^2 = g^2(2g + 1) 14g + 7 = 7(2g + 1) Now, we can factor out (2g + 1) from both expressions. So, the factored form of 2g^3 + g^2 + 14g + 7 is (g^2 + 7)(2g + 1).

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Factor. $\newline$ $2g^3 + g^2 + 14g + 7$

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Q. Factor.

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2g^3 + g^2 + 14g + 7

Identify Common Factors: Look for common factors in each pair of terms. We will first group the terms into pairs and look for common factors in each pair. Grouping: $(2g^3 + g^2)$ and $(14g + 7)$ .
Factor First Group: Factor out the common factor from the first group. $\newline$ In the first group $2g^3 + g^2$ , the common factor is $g^2$ . $\newline$ Factoring out $g^2$ gives us $g^2(2g + 1)$ .
Factor Second Group: Factor out the common factor from the second group. $\newline$ In the second group $(14g + 7)$ , the common factor is $7$ . $\newline$ Factoring out $7$ gives us $7(2g + 1)$ .
Write Factored Expression: Write the factored form of the entire expression. $\newline$ We have found: $\newline$ $2g^3 + g^2 = g^2(2g + 1)$ $\newline$ $14g + 7 = 7(2g + 1)$ $\newline$ Now, we can factor out $(2g + 1)$ from both expressions. $\newline$ So, the factored form of $2g^3 + g^2 + 14g + 7$ is $(g^2 + 7)(2g + 1)$ .