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(a+b)(a-b) Expansion and Visualisation

Find the HCF ...

Question

Find the HCF of the following pair of polynomials:
$x^{2} + 2 x - 15$ and $x^{2} - 7 x + 12$

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Solution

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

Factorise $x^{2} + 2 x - 15$ as follows:

$x^{2} + 2 x - 15 = x^{2} + 5 x - 3 x - 15 = x (x + 5) - 3 (x + 5) = (x - 3) (x + 5)$

Now, factorise $x^{2} - 7 x + 12$ as follows:

$x^{2} - 7 x + 1 = x^{2} - 4 x - 3 x + 12 = x (x - 4) - 3 (x - 4) = (x - 3) (x - 4)$

Since the common factor between the polynomials $x^{2} + 2 x - 15$ and $x^{2} - 7 x + 12$ is $(x - 3)$ .

Hence, the $H C F$ is $(x - 3)$ .

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