Factorise by splitting the middle term x²+3√7x+14

Hello!

We'll split the middle term, $\displaystyle{3}\sqrt{{{7}}}{x},$ as $\displaystyle\sqrt{{{7}}}{x}+{2}\sqrt{{{7}}}{x}.$ Then

$\displaystyle{{x}}^{{2}}+{3}\sqrt{{{7}}}{x}+{14}={{x}}^{{2}}+\sqrt{{{7}}}{x}+{2}\sqrt{{{7}}}{x}+{14}=$

$\displaystyle={x}{\left({x}+\sqrt{{{7}}}\right)}+{2}\sqrt{{{7}}}{\left({x}+\sqrt{{{7}}}\right)}={\left({x}+{2}\sqrt{{{7}}}\right)}{\left({x}+\sqrt{{{7}}}\right)}.$

This is the answer. We used the fact that $\displaystyle{14}={2}\sqrt{{{7}}}\cdot\sqrt{{{7}}}.$

Ninenotes

Wednesday, January 26, 2011

Factorise by splitting the middle term x²+3√7x+14

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