To add polynomials, we add ______ terms, So (3x^2+2x+4)+(8x^2-x+1)=

sodni3 2021-09-03 Answered

To add polynomials, we add ______ terms, So

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

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Anonym
Answered 2021-09-04 Author has 25748 answers
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
\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={11}{x}^{{2}}+{x}+{5}\)
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