Question

x^5 + 4x^3 - 5x

Answer 1

\(=x^5-x^3+5x^3-5x\)

\(=x^3\left(x^2-1\right)-5x\left(x^2-1\right)\)

\(=x\left(x-1\right)\left(x+1\right)\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)

Answer 2

\(x^5+4x^3-5x=0\)

\(\Leftrightarrow x^3\cdot\left(x^2-1\right)-5x\cdot\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\cdot\left(x^3-5x\right)=0\)

\(\Leftrightarrow\left(x-1\right)\cdot\left(x+1\right)\cdot x\cdot\left(x^2-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\\x=0\\x^2-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=0\\x=\sqrt{5}\end{matrix}\right.\)

Answer 3

\(x^5+4x^3-5x\)

\(=x\left(\frac{x^5}{x}+\frac{4x^3}{x}-\frac{5x}{x}\right)\)

\(=x\left(x^2-1\right)\left(x^2+5\right)\)

\(=x\left(x+1\right)\left(x-1\right)\left(x^2+5\right)\)

Answer 4

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Answer 5

x⁵ + 4x³ - 5x

=x( x⁴ + 4x² - 5 )

=x( x²-1 )( x²+5 )

=x( x-1)(x+1)(x²+5)