[tex] \large \mathcal{ANSWER:} [/tex]
[tex] \boxed{\boxed{x(x + 5)(2x - 1)(x^2 + 1)}} [/tex]
[tex] \large \mathcal{SOLUTION:} [/tex]
[tex] \begin{array}{l} 2x^5 + 9x^4 - 3x^3 + 9x^2 - 5x \\ \\ = x(2x^4 + 9x^3 - 3x^2 + 9x - 5) \\ \\ \underline{\textsf{Break}\: -3x^2\:\textsf{into}\: -5x^2 + 2x^2.} \\ \\ = x(2x^4 + 9x^3 - 5x^2 + 2x^2 + 9x - 5) \\ \\ \underline{\textsf{Factor by grouping.}} \\ \\ = x\left[x^2(2x^2 + 9x - 5) + (2x^2 + 9x + 5)\right] \\ \\ = x(2x^2 + 9x - 5)(x^2 + 1) \\ \\ = x(x + 5)(2x - 1)(x^2 + 1) \quad \checkmark \\ \\ \footnotesize x^2 + 1\:\textsf{is not factorable.} \end{array} [/tex]
[tex] \texttt \color{cyan} {\#CarryOnLearning} [/tex]
