Question

Factorise : (i) x³+13x²+32+20.

Answer 1

Answer:

Let p(x)=

${x}^{3} + {13x}^{2} + 32x + 20$

p(-1)=-1+13-32+20

=33-33

=0

Therefore (x+1) is a factor of p(x)

On dividing p(x) by (x+1),we get :-

p(x)÷(x+1)=

${x}^{2} + 12x + 20$

Thus,

${x}^{3} + {13x}^{2} + 32x + 20 =( x + 1)( {x}^{2} + 12x + 20$)

$= (x + 1)( {x}^{2} + 10x + 2x + 20$)

$= </em></strong><strong><em>(x + 1)</em></strong><strong><em>{</em></strong><strong><em>x(x + 10) + 2(x + 10)$)}

$= (x + 1)(x + 2)(x + 10)$)

Hence,

${x}^{3} + 13 {x}^{2} + 32x + 20 = (x + 1)(x + 2)(x + 10).$

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