Question

# What are the linear and quadratic factors of the expression

Factors and multiples
What are the linear and quadratic factors of the expression $$\displaystyle{8}{x}^{{{4}}}-{8}{x}$$

2021-08-13
Given: $$\displaystyle{8}{x}^{{{4}}}-{8}{x}$$
$$\displaystyle{8}{x}{\left({x}^{{{3}}}-{1}\right)}$$
$$\displaystyle{x}^{{{3}}}-{1}={\left({x}-{1}\right)}{\left({x}^{{{2}}}+{x}+{1}\right)}$$
$$\displaystyle={8}{x}{\left({x}-{1}\right)}{\left({x}^{{{2}}}+{x}+{1}\right)}$$
Step 2
Linear factor $$\displaystyle={x},{\left({x}-{1}\right)}$$
quadratic factor $$\displaystyle={\left({x}^{{{2}}}+{x}+{1}\right)}$$