# use long division to determine if 2x-1 is a factor of p(x)=6x^3+7x^2-x-2

use long division to determine if 2x-1 is a factor of $$\displaystyle{p}{\left({x}\right)}={6}{x}^{{3}}+{7}{x}^{{2}}-{x}-{2}$$

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averes8

$$\displaystyle{6}{x}^{{3}}+{7}{x}^{{2}}-{x}-{2}$$ \ 2x-1
$$\displaystyle-{6}{x}^{{3}}+{3}{x}^{{2}}$$ \ $$\displaystyle{3}{x}^{{2}}+{5}{x}+{2}$$
$$\displaystyle{10}{x}^{{2}}-{x}-{2}$$
$$\displaystyle-{10}{x}^{{2}}+{5}{x}$$
$$4x-2$$
$$-4x+2$$
$$(2x-1)$$ in a .... of p(x)
$$\displaystyle{p}{\left({x}\right)}={\left({2}{x}-{1}\right)}{\left({3}{x}^{{2}}+{5}{x}+{2}\right)}$$