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If you divide 52, you will obtain 2 as the quotient and 1 as the remainder.
 
Also here 5 is the dividend, 2 is the divisor, 2 is the quotient, and 1 is the remainder.
 
So we can write 5=(2×2)+1
 
or Dividend \(=\) (Divisor \(×\) Quotient) \(+\) Remainder
 
Note that the remainder is always less than the divisor.
In algebra, long division polynomial is an algorithm for dividing a polynomial by a same or lower degree polynomial, a generally used version of the common arithmetic technique known as long division.
 
Let’s try to divide the two polynomials.
Example:
 p(xq(x where p(x) =2x3+x2+xq(x) =x.
 
\((2x^3 + x^2 +x) ÷ x\)
 
\(=\) \(\frac {2x^3}{x}+\) \(\frac{x^2}{x}+\)\(\frac{x}{x}\)
 
\(=\) \(2x^2\) \(+\) \(x\) \(+\) \(1\).
 
In here, \((2x^3 + x^2 +x)\) is the dividend, \(x\) is the divisor, \(2x^2\) \(+\) \(x\) \(+\) \(1\) is the quotient and \(0\) is the remainder.
 
Note that the remainder is \(0\) as the polynomial \(q(x)\) divides the polynomial \(p
(x)\) without any remainder.
 
Important!
In this case, x is common to each term of 2x3+x2+x. So we can write 2x3+x2+x as x2x2+x+1.
 
We say that x and  2x2+x+1 are factors of 2x3+x2+x, and 2x3+x2+x is a multiple of x as well as a multiple of 2x2+x+1.
Example:
Example: