Question

Factorise : root 5x square + 2x - 3root 5

Answer 1

$\textbf{Given:}$

$\mathsf{\sqrt{5}x^2+2x-3\sqrt{5}}$

$\textbf{To find:}$

$\textsf{Factors of}$

$\mathsf{\sqrt{5}x^2+2x-3\sqrt{5}}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{7cm} \\\textsf{The method of wrriting the given polynomial}\\\\\textsf{into product of its factors is called Factorisation}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{\sqrt{5}x^2+2x-3\sqrt{5}}$

$\mathsf{=\sqrt{5}x^2+5x-3x-3\sqrt{5}}$

$\mathsf{=\sqrt{5}x(x+\sqrt{5})-3(x+\sqrt{5})}$

$\mathsf{=(\sqrt{5}x-3)\,(x+\sqrt{5})}$

$\implies\boxed{\mathsf{\sqrt{5}x^2+2x-3\sqrt{5}=(\sqrt{5}x-3)\,(x+\sqrt{5})}}$

$\textbf{Find more:}}$

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