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

Isa Trevino 2021-08-31 Answered
Find the sum of the polynomials:
\(\displaystyle{8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\) and \(\displaystyle{3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Anonym
Answered 2021-09-01 Author has 24895 answers
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:
\(\displaystyle{3}{x}^{{4}}+{6}{x}^{{3}}-{x}^{{2}}+{7}{x}-{2}\)
Not exactly what you’re looking for?
Ask My Question
7
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...