Which one of the following is a factor of
$2 x^{3} y + 4 x y^{2} + 8 x y ?$

2 x y

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2 x^{2} y

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4 x^{3}

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Solution

The correct option is A $2 x y$
Given: $2 x^{3} y + 4 x y^{2} + 8 x y .$
Now, each term can be factorised as,
$2 x^{3} y = 2 \times x \times x \times x \times y$
$4 x y^{2} = 2 \times 2 \times x \times y \times y$
$8 x y = 2 \times 2 \times 2 \times x \times y$
In above terms 2, x and y are the common terms.
So,
$2 x^{3} y + 4 x y^{2} + 8 x y$
$= 2 x y (x^{2} + 2 y + 4)$
$∴ 2 x y$ is one of the factors of $2 x^{3} y + 4 x y^{2} + 8 x y$ .

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