Given:
[tex]\frac{x^3+2x^2+2x+1}{x+1}[/tex]
Required:
We need to find the quotient.
Explanation:
[tex]Numerator\text{ -}x^3+2x^2+2x+1[/tex][tex]Denominator-x+1.[/tex]
The degree of the denominator is 1.
The number of rows = 1+1=2.
The degree of the numerator is 3.
The niumber of columns = 3-1+1 =3.
[tex]Use\text{ }x\times x^2=x^3.[/tex][tex]Use\text{ 1}\times1=1.[/tex]
[tex]2x^2-x^2=x^2\text{ and use x}\times x=x^2.\text{ }[/tex]
The quotient of the polynomials
[tex]x^2+x+1[/tex]
Final answer:
[tex]\frac{x^3+2x^2+2x+1}{x+1}=x^2+x+1[/tex]
