Factorise: $3 x^{4} + 6 x^{3} y + 9 x^{z}$

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Solution

Let us first find the HCF of all the terms of the given polynomial $3 x^{4} + 6 x^{3} y + 9 x^{2}$ by factoring the terms as follows:

$3 x^{4} = 3 \times x \times x \times x \times x 6 x^{3} y = 2 \times 3 \times x \times x \times x \times y 9 x^{2} = 3 \times 3 \times x \times x$

Therefore, $H C F = 3 \times x \times x = 3 x^{2}$

Now, we factor out the HCF from each term of the polynomial $3 x^{4} + 6 x^{3} y + 9 x^{2}$ as shown below:

$3 x^{4} + 6 x^{3} y + 9 x^{2} = 3 x^{2} (x^{2} + 2 x y + 3)$

Hence, $3 x^{4} + 6 x^{3} y + 9 x^{2} = 3 x^{2} (x^{2} + 2 x y + 3)$ .

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