# Find the sum of the polynomials: 8x^3-2x^2+6x-2 and 3x^4-2x^3+x^2+x

Find the sum of the polynomials:
$$\displaystyle{8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}$$ and $$\displaystyle{3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}$$

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Anonym
To find the sum of polynomials: $$\displaystyle{8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}$$ and $$\displaystyle{3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}$$
Solution:
$$\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}$$
On simplifying further we get:
$$\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{8}{x}^{{3}}-{2}{x}^{{3}}-{2}{x}^{{2}}+{x}^{{2}}+{6}{x}+{x}-{2}$$
$$\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{\left({8}{x}^{{3}}-{2}{x}^{{3}}\right)}-{\left({2}{x}^{{2}}-{x}^{{2}}\right)}+{\left({6}{x}+{x}\right)}-{2}$$
$$\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{6}{x}^{{3}}-{x}^{{2}}+{7}{x}-{2}$$
Result:
Required expression is:
$$\displaystyle{3}{x}^{{4}}+{6}{x}^{{3}}-{x}^{{2}}+{7}{x}-{2}$$