# Find all the roots (real and imaginary) of the given polynomials. Describe multiplicity when applicable. f(x)=x^4-8x^2-8x+15

Find all the roots (real and imaginary) of the given polynomials. Describe multiplicity when applicable. Please show all work and simplify your answers.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}$$

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Given $$\displaystyle{f{{\left({x}\right)}}}={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}$$
The all the roots of the above expression is
X=1
X=3
X=-2+i
X=-2-i
$$\displaystyle={\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}+{2}-{i}\right)}{\left({x}+{2}+{i}\right)}$$
$$\displaystyle={\left({x}^{{2}}-{3}{x}-{x}+{3}\right)}{\left({x}^{{2}}+{2}{x}+\xi+{2}{x}+{4}+{2}{i}-\xi-{2}{i}+{1}\right)}$$
$$\displaystyle={\left({x}^{{2}}-{4}{x}+{3}\right)}{\left({x}^{{2}}+{4}{x}+{5}\right)}$$
$$\displaystyle={\left({x}^{{4}}+{4}{x}^{{3}}+{5}{x}^{{2}}-{4}{x}^{{3}}-{16}{x}^{{2}}-{20}{x}+{3}{x}^{{2}}+{12}{x}+{15}\right)}$$
$$\displaystyle={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}$$