Solve: $8 x^{2} - 72 x y + 12 x$

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Solution

We first factorize each term of the given polynomial $8 x^{2} - 72 x y + 12 x$ as shown below:

$8 x^{2} = 2 \times 2 \times 2 \times x \times x 72 x y = 2 \times 2 \times 2 \times 3 \times 3 \times x \times y 12 x = 2 \times 2 \times 3 \times x$
The common factors of $8 x^{2}, 72 x y$ and $12 x$ are $2, 2$ and $x$ , therefore, the HCF is:

$2 \times 2 \times x = 4 x$

Thus, taking out the HCF, we have:

$8 x^{2} - 72 x y + 12 x = 4 x (2 x - 18 y + 3)$

Hence, $8 x^{2} - 72 x y + 12 x = 4 x (2 x - 18 y + 3)$ .

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