Question

factor completely. \\(4g^{3} + 8g^{2} + 17g + 34\\)

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(4g^3 + 8g^2) + (17g + 34)$

Step2: Factor out GCF from each group

Factor out $4g^2$ from the first group and $17$ from the second group: $4g^2(g + 2) + 17(g + 2)$

Step3: Factor out the common binomial factor

Factor out $(g + 2)$ from both terms: $(g + 2)(4g^2 + 17)$

Answer:

$(g + 2)(4g^2 + 17)$