Question

factor by grouping.
$3x^5 + 2x^3 + 21x^2 + 14$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(3x^5 + 2x^3) + (21x^2 + 14)$

Step2: Factor out GCF from each group

For the first group, factor out $x^3$: $x^3(3x^2 + 2)$
For the second group, factor out $7$: $7(3x^2 + 2)$

Step3: Factor out the common binomial factor

Now, factor out $(3x^2 + 2)$ from both terms: $(3x^2 + 2)(x^3 + 7)$

Answer:

$(3x^2 + 2)(x^3 + 7)$