Find the HCF of the following pair of polynomials:
$x^{2} - x y$ and $x^{2} - y^{2}$

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Solution

We know that $H C F$ is the highest common factor.

Factorise $x^{2} - x y$ as follows:

$x^{2} - x y = x (x - y)$

Now, factorise $x^{2} - y^{2}$ as follows:

$x^{2} - y^{2} = (x + y) (x - y)$ (using identity $a^{2} - b^{2} = (a + b) (a - b)$ )

Since the common factor between the polynomials $x^{2} - x y$ and $x^{2} - y^{2}$ is $(x - y)$ .

Hence, the $H C F$ is $(x - y)$ .

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Question 1
Classify the following polynomials as polynomials in one variable, two variables etc.

(i) $x^{2} + x + 1$

(ii) $y^{3} - 5 y$

(iii) $x y + y z + z x$

(iv) $x^{2} - x y + y^{2} + 1$

Question 1
Classify the following polynomials as polynomials in one variable, two variables etc.

(i) $x^{2} + x + 1$

(ii) $y^{3} - 5 y$

(iii) $x y + y z + z x$

(iv) $x^{2} - x y + y^{2} + 1$

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Find the HCF of the following pair of polynomials:x2−xy and x2−y2

We know that HCF is the highest common factor.Factorise x2−xy as follows:x2−xy=x(x−y)Now, factorise x2−y2 as follows:x2−y2=(x+y)(x−y) (using identity a2−b2=(a+b)(a−b))Since the common factor between the polynomials x2−xy and x2−y2 is (x−y).Hence, the HCF is (x−y).

Find the HCF of the following pair of polynomials:
$x^{2} - x y$ and $x^{2} - y^{2}$