Find the HCF of the following pairs of polynomials:
$5 x - 10$ and $5 x^{2} - 20$

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Solution

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

Factorise $5 x - 10$ as follows:

$5 x - 10 = 5 (x - 2)$

Now, factorise $5 x^{2} - 20$ as follows:

$5 x^{2} - 20 = 5 (x^{2} - 4) = 5 (x - 2) (x + 2)$ (using identity $a^{2} - b^{2} = (a + b) (a - b)$ )

Since the common factor between the polynomials $5 x - 10$ and $5 x^{2} - 20$ is $5 (x - 2)$ .

Hence, the $H C F$ is $5 (x - 2)$ .

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