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Factor completely.

x^(4)+5x^(3)+4x+20=

Factor completely.\newlinex4+5x3+4x+20= x^{4}+5 x^{3}+4 x+20=

Full solution

Q. Factor completely.\newlinex4+5x3+4x+20= x^{4}+5 x^{3}+4 x+20=
  1. Identify Grouping Possibilities: Step Title: Identify Grouping Possibilities\newlineConcise Step Description: Look for a way to group terms in the polynomial to factor by grouping.\newlineStep Calculation: Group x4x^4 and 5x35x^3 together, and 4x4x and 2020 together.\newlineStep Output: (x4+5x3)+(4x+20)(x^4 + 5x^3) + (4x + 20)
  2. Factor Out Common Factors: Step Title: Factor Out Common Factors from Each Group\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: Factor x3x^3 from the first group and 44 from the second group.\newlineStep Output: x3(x+5)+4(x+5)x^3(x + 5) + 4(x + 5)
  3. Factor Out the Common Binomial: Step Title: Factor Out the Common Binomial\newlineConcise Step Description: Factor out the common binomial factor from the two groups.\newlineStep Calculation: Factor out (x+5)(x + 5) from both groups.\newlineStep Output: (x+5)(x3+4)(x + 5)(x^3 + 4)
  4. Check for Further Factoring: Step Title: Check for Further Factoring\newlineConcise Step Description: Check if the remaining terms can be factored further.\newlineStep Calculation: x3+4x^3 + 4 cannot be factored further using real numbers.\newlineStep Output: No further factoring possible.