We know that to add polynomial we add similar terms.

Example:

\(\displaystyle{\left({x}+{2}\right)}+{\left({x}^{{2}}+{3}{x}+{4}\right)}={x}+{2}+{x}^{{2}}+{3}{x}+{4}\)

\(\displaystyle={x}^{{2}}+{3}{x}+{x}+{2}+{4}\)

\(\displaystyle={x}^{{2}}+{4}{x}+{6}\)

Here we have combined the terms x with x and constants with constants.

Applying addition property of the polynomial for the given expression, we get

\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={3}{x}^{{2}}+{2}{x}+{4}+{8}{x}^{{2}}-{x}+{1}\)

\(\displaystyle={3}{x}^{{2}}+{8}{x}^{{2}}+{2}{x}-{x}+{4}+{1}\)

\(\displaystyle={11}{x}^{{2}}+{x}+{5}\)

Hence, we can fill in the blanks:

To add polynomials, we add similar terms. So

\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={11}{x}^{{2}}+{x}+{5}\)

Example:

\(\displaystyle{\left({x}+{2}\right)}+{\left({x}^{{2}}+{3}{x}+{4}\right)}={x}+{2}+{x}^{{2}}+{3}{x}+{4}\)

\(\displaystyle={x}^{{2}}+{3}{x}+{x}+{2}+{4}\)

\(\displaystyle={x}^{{2}}+{4}{x}+{6}\)

Here we have combined the terms x with x and constants with constants.

Applying addition property of the polynomial for the given expression, we get

\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={3}{x}^{{2}}+{2}{x}+{4}+{8}{x}^{{2}}-{x}+{1}\)

\(\displaystyle={3}{x}^{{2}}+{8}{x}^{{2}}+{2}{x}-{x}+{4}+{1}\)

\(\displaystyle={11}{x}^{{2}}+{x}+{5}\)

Hence, we can fill in the blanks:

To add polynomials, we add similar terms. So

\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={11}{x}^{{2}}+{x}+{5}\)