Question

Factorise:$\sqrt{3}{x}^2+4x-7\sqrt{3}$

Answer 1

The given expression is $\sqrt{3}{x}^2+4x-7\sqrt{3}$

We are asked to factorise the given expression.

We can factorise the given expression by rewriting it and taking out common terms.

$\sqrt{3}{x}^2+4x-7\sqrt{3}$

The expression can be written as:

$\sqrt{3}{x}^2-3x+7x-7\sqrt{3}$

$\Rightarrow \sqrt{3}{x}^2-\sqrt{3}\times \sqrt{3}x+7x-7\sqrt{3}$

Taking out $\sqrt{3}x$ common from the first two terms and $7$ from the last two.

$\Rightarrow \sqrt{3}x(x-\sqrt{3})+7(x-\sqrt{3})$

$\Rightarrow (\sqrt{3}x+7)(x-\sqrt{3})$

Thus, $(\sqrt{3}x+7)and(x-\sqrt{3})$ are the factors of the given expression.

Hence, $\sqrt{3}{x}^2+4x-7\sqrt{3}=(\sqrt{3}x+7)(x-\sqrt{3})$