Question

factorise x ^ 3 + 2x ^ 2 - 5x - 6​

Answer 1

Question :-

Factorise x³ + 2x² - 5x - 6

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Solution :-

➲ Given Information :-

• Polynomial ➣$\rm{ {x}^{3} + {x}^{2} + {x}^{2} - 5x - 6}$

➲ To Find :-

• Factorise the polynomial

➲ Concept Used :-

• Factorisation
• Mid-term splitting method
• Grouping method

➲ Explanation :-

• Firstly, we'll split the mid term and then group the rest, after some minute calculations, we'll get our answer. Now let's proceed towards our calculation.

➲ Calculation :-

∵ Our polynomial was,$\rm{ {x}^{3} + {x}^{2} + {x}^{2} - 5x - 6}$

∴ Splitting up the middle term, We get,

$\rm{ : \implies \: {x}^{3} + {x}^{2} + {x}^{2} - 5x - 6}$

Grouping the terms, We get,

$\rm: \implies \: {x}^{2} (x + 1) + {x}^{2} + x - 6x - 6$

Calculating further, We get,

$\rm: \implies \: {x}^{2} (x + 1) + x(x + 1) - 6(x + 1)$

Grouping again, We get,

$\rm: \implies \:(x + 1)( {x}^{2} + x - 6)$

Now, again splitting the mid term, We get,

$\rm : \implies \: (x + 1) ( {x}^{2} + 3x - 2x - 6)$

Now, again grouping, We get,

$\rm: \implies \: (x + 1)[x(x + 3) - 2(x + 3)]$

Now, here's our answer,

$\rm: \implies \boxed{\boxed{ \bf \red{(x + 1)( x + 3)(x - 2)}}}$

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Final Answer :-

After factorising, The answer is,

• $\boxed{\boxed{ \bf \red{(x + 1)( x + 3)(x - 2)}}}$

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