Factor completely. $\newline$ $x^{4}+5 x^{3}+4 x+20=$

Full solution

Q. Factor completely.

\newline

x^{4}+5 x^{3}+4 x+20=

Identify Grouping Possibilities: Step Title: Identify Grouping Possibilities $\newline$ Concise Step Description: Look for a way to group terms in the polynomial to factor by grouping. $\newline$ Step Calculation: Group $x^4$ and $5x^3$ together, and $4x$ and $20$ together. $\newline$ Step Output: $(x^4 + 5x^3) + (4x + 20)$
Factor Out Common Factors: Step Title: Factor Out Common Factors from Each Group $\newline$ Concise Step Description: Factor out the greatest common factor from each group. $\newline$ Step Calculation: Factor $x^3$ from the first group and $4$ from the second group. $\newline$ Step Output: $x^3(x + 5) + 4(x + 5)$
Factor Out the Common Binomial: Step Title: Factor Out the Common Binomial $\newline$ Concise Step Description: Factor out the common binomial factor from the two groups. $\newline$ Step Calculation: Factor out $(x + 5)$ from both groups. $\newline$ Step Output: $(x + 5)(x^3 + 4)$
Check for Further Factoring: Step Title: Check for Further Factoring $\newline$ Concise Step Description: Check if the remaining terms can be factored further. $\newline$ Step Calculation: $x^3 + 4$ cannot be factored further using real numbers. $\newline$ Step Output: No further factoring possible.