IMathAS-libretexts

Polynomials Mini-Lesson Review
The table below shows the steps that a student used to simplify three polynomial expressions. For each problem, identify the mistake (if it exists).
$\displaystyle {\left({2}{x}^{{2}}+{3}\right)}+{\left({3}{x}^{{2}}+{5}\right)}$ $\displaystyle {2}{x}^{{2}}+{3}+{3}{x}^{{2}}+{5}$ $\displaystyle {2}{x}^{{2}}+{3}{x}^{{2}}+{3}+{5}$ $\displaystyle {5}{x}^{{4}}+{8}$ All steps are correct	$\displaystyle {\left({3}{z}^{{3}}+{4}{z}^{{2}}+{2}\right)}+{\left({3}{z}^{{2}}-{8}\right)}$ $\displaystyle {3}{z}^{{3}}+{4}{z}^{{2}}+{2}+{3}{z}^{{2}}-{8}$ $\displaystyle {3}{z}^{{3}}+{4}{z}^{{2}}+{3}{z}^{{2}}+{2}-{8}$ $\displaystyle {3}{z}^{{3}}+{7}{z}^{{2}}-{6}$ All steps are correct	$\displaystyle {\left({4}{a}^{{2}}-{3}\right)}-{\left({2}{a}^{{2}}+{6}\right)}$ $\displaystyle {4}{a}^{{2}}-{3}-{2}{a}^{{2}}+{6}$ $\displaystyle {4}{a}^{{2}}-{2}{a}^{{2}}-{3}+{6}$ $\displaystyle {2}{a}^{{2}}+{3}$ All steps are correct