Question

Find the quotient and remainder on dividing $x^{2} - 2 x y + y^{2}$ by $x - y$ .

Accepted Answer

The given polynomials are $x^{2} - 2 x y + y^{2}$ and $x - y$ .

We need to find the quotient and remainder on dividing polynomial $x^{2} - 2 x y + y^{2}$ by $x - y$ .

Here, dividend $= x^{2} - 2 x y + y^{2}$ and divisor $= x - y$

Steps for dividing polynomial from another polynomial using long division method:

$1 .$ Make sure the polynomial is written in descending order. If any term is missing, use a zero to fill in the missing term.

$2 .$ Divide the term with the highest power of dividend by term with the highest power of divisor.

$3 .$ Take the answer obtained in the previous step as quotient and multiply to divisor.

$4 .$ Write the answer obtained in the previous step under the terms of dividend. Now, subtract and bring down the next term.

$5 .$ Repeat steps $2, 3,$ and $4$ until there are no more terms to bring down.

$\begin{matrix} x & - & y & x^{2} & - & 2 x y & + & y^{2} & x & - & y \\ x^{2} & - & x y \\ (-) & (+) \\ - & x y & + & y^{2} \\ - & x y & + & y^{2} \\ (+) & (-) \\ 0 \end{matrix}$

Hence, quotient is $x - y$ and remainder is $0$ .

Chhattisgarh Board Solutions for Exercise 4: Exercise – 1

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Exercise 4: Exercise – 1

Questions from Chhattisgarh Board Solutions for Exercise 4: Exercise – 1 with Hints & Solutions

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