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# Factorise : (iii) x ^3 + 13 x ^2 + 13 x + 20

5.(iii)  Factorise :

(iii)    $x^3 + 13x^2 + 32x + 20$

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Given polynomial is  $x^3 + 13x^2 + 32x + 20$

Now, by hit and trial method we observed that  $(x+1)$  is one of the factore of given polynomial.

By long division method, we will get

We know that  Dividend = (Divisor $\times$ Quotient) + Remainder

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

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

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

Therefore, on factorization of  $x^3 + 13x^2 + 32x + 20$ we will get  $(x+1)(x+10)(x+2)$

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