Factor by grouping.
$4 w^{3} + 3 w^{2} + 8 w + 6$

Answer

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Answer

Final Answer: The factored form of the expression is $(4 w + 3) (w^{2} + 2)$ .

Steps

Step 1 ：The expression given is $4 w^{3} + 3 w^{2} + 8 w + 6$ .

Step 2 ：We can factor this expression by grouping the terms two at a time.

Step 3 ：First, we group the terms as $(4 w^{3} + 3 w^{2}) + (8 w + 6)$ .

Step 4 ：Then, we factor out the greatest common factor from each group.

Step 5 ：From the first group, we can factor out $w^{2}$ to get $w^{2} (4 w + 3)$ .

Step 6 ：From the second group, we can factor out 2 to get $2 (4 w + 3)$ .

Step 7 ：Now, we can see that $(4 w + 3)$ is a common factor.

Step 8 ：So, the factored form of the expression is $(4 w + 3) (w^{2} + 2)$ .

Step 9 ：Final Answer: The factored form of the expression is $(4 w + 3) (w^{2} + 2)$ .