Question

Add the polynomials.
\(\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}\)

Answer 1

A polynomial in a variable x is a function of the form \(\displaystyle{a}_{{n}}{x}^{{n}}+{a}_{{{n}-{1}}}{x}^{{{n}-{1}}}+\ldots+{a}_{{1}}{x}+{a}_{{0}}\). This polynomial has degree n. The constants \(\displaystyle{a}_{{i}}\) are the coefficients and are constants.
To add two polynomials we add like terms, that is, add terms of the same degree. For example \(\displaystyle{2}{x}^{{2}},{4}{x}^{{2}}\) are terms of the same degree but the terms \(\displaystyle{2}{x}^{{2}},{4}{x}^{{3}}\) are terms of different degree.
The sum to be computed is \(\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}\). . Drop the parenthesis and combine like terms.
\(\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}={7}{x}^{{2}}-{6}{x}+{3}{x}^{{3}}-{9}{x}\)
\(\displaystyle={3}{x}^{{3}}+{7}{x}^{{2}}+{\left(-{6}{x}-{9}{x}\right)}+{6}\)
\(\displaystyle={3}{x}^{{3}}+{7}{x}^{{2}}-{15}{x}+{6}\)
Hence, the sum is \(\displaystyle{3}{x}^{{3}}+{7}{x}^{{2}}-{15}{x}+{6}\).