Question

EllØ❤

Factorise :-
${x}^{2} + \sqrt[3]{3x} + 6$
❤_____Gunnie_______❤​

Answer 1

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: QUESTION \: \: \mid}}}}}}$

$\bold{To \: \: Factorise \: :}$ $\boxed{\boxed{\bold{ x {}^{2} + 3 \sqrt{3} x + 6 }}}$



$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: ANSWER\: \: \mid}}}}}}$

$\bold{ The \: \: factors \: \: are \: \: : \: \: (x + \sqrt{3} ) \: \: and \: \: (x + 2 \sqrt{3} ) \: \: }$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: SOLUTION \: \: \mid}}}}}}$

$\underline{ \underline{ \pink{\bold{ \: \: Step - By - Step - Explaintion \: \: }}}}$

$\underline{ \green{ \bold{METHOD \: \: USE : }}} \\ \\ \: \: \: \: \: \: \: \: \underline{ \boxed{ \bold{ \blue{ \: \: Spilting \: \: Middle \: \: Term \: \: \: } }}}$

$\bold{1st \: \: term \: \: is \: \: x {}^{2} \: \: \: ,\: \: coeffient = 1} \\ \\ \bold{Middle \: \: term \: \: is \: \: 3 \sqrt{3}x \: \: ,\: \: coefficen t = 3 \sqrt{3} } \\ \\ \bold{Last \: \: term \: (constant) = 6}$

$\underline{\bold{ \: \: Step \: \: 1. \: \: }} \\ \\ \bold{Multiply \: \:t he \: \: first \: \: term \: \: with \: \: the \: \: constan t \: \: } \\ \\ \boxed{\bold{1 \times 6 = 6}}$

$\underline{ \bold{ \: \: Step \: \: 2. \: \: }} \\ \\ \bold{Find \: \: the \: \: product \: \: of \: \: 6 \: \: whose \: \: sum \: \: } \\ \bold{is \: \: equal \: \: to \: \: the \: \: coefficient \: \: of \: \: the} \\ \bold{middle \: \: term \:, \: which \: \: is \: \: 3 \sqrt{3} \: .} \\ \\ \bold{We\: \: \: found \: \: the \: \: products\: \: are \: : } \\ \\ \bold{2 \sqrt{3} \: \: and \: \: \sqrt{3} \: \: \: \: ,\: \: As \: \: \: \: 2\sqrt{3} + \sqrt{3} = 3 \sqrt{3} } \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \sqrt{3 } \times \sqrt{3 } = 6}$

$\underline{ \bold{ \: \: Step \: \: 3. \: \: }} \\ \\ \bold{Rewrite \: \: the \: \: polynomial \: \: by \: \: spilting} \\ \bold{middle \: \: term} \\ \\ \bold{x {}^{2} + 3 \sqrt{3}x + 6 } \\ \\ \bold{ = \: \underline{ \: x {}^{2} + 2 \sqrt{3} + \sqrt{3} + 6 \: \: }}$

$\underline{ \bold{ \: \: Step \: \: 4. \: \: }} \\ \\ \bold{Add \: \: up \: \: the \: \: first \: \:two\: \: term \: \: by} \\ \bold{pulling \: \: out \: \: like \: \: factors} \\ \\ \bold{i.e \: \: \: \: \: \: \: \underline{ \: \: x(x + 2 \sqrt{3}) \: \: }} \\ \\ \\ \bold{Add \: \: up \: \: the \: \: second\: \:two\: \: term \: \: by} \\ \bold{pulling \: \: out \: \: like \: \: factors} \\ \\ \bold{i.e \: \: \: \: \underline{ \: \: \sqrt{3}(x + 2 \sqrt{3}) \: \: }}$

$\underline{ \bold{ \: \: Step \: \: 5. \: \: }} \\ \\ \bold{Add \: \: up \: \: the \: \: four \: \: term \: \: of \: \: \underline{ \: \: Step \: \: 4. \: \: }} \\ \\ \\ \bold{x(x +2 \sqrt{3} ) + \sqrt{3}(x + 2 \sqrt{3} ) } \\ \\ \bold{ = (x + \sqrt{3} )(x + 2 \sqrt{3} )}$

$\bold{Hence,} \\ \\ \boxed{\bold{x {}^{2} + 3 \sqrt{3} x + 6 = (x + \sqrt{3})(x + 2 \sqrt{3} ) }}$

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✝$\mathfrak{ \red{THANKS..}}$✝

Answer 2

Answer:

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