Find the HCF of the following pair of polynomials:
$2 x^{2} + x$ and $4 x^{2} - 1$

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Solution

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

Factorise $2 x^{2} + x$ as follows:

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

Now, factorise $4 x^{2} - 1$ as follows:

$4 x^{2} - 1 = (2 x + 1) (2 x - 1)$ (using identity $a^{2} - b^{2} = (a + b) (a - b)$ )

Since the common factor between the polynomials $2 x^{2} + x$ and $4 x^{2} - 1$ is $(2 x + 1)$ .

Hence, the $H C F$ is $(2 x + 1)$ .

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