Answer :

Let, f (x) = x3+13x2+32x+20

The factors of the constant term + 20 are


Putting x = -1, we have


f (-1) = (-1)3 + 13 (-1)2 + 32 (-1) + 20


= -1 + 13 – 32 + 20


= 0


So, (x + 1) is a factor of f (x)


Let us now divide


f (x) = x3+13x2+32x+20 by (x + 1) to get the other factors of f (x)


Using long division method, we get


x3+13x2+32x+20 = (x + 1) (x2 + 12x + 20)


x2 + 2x + 20 = x2 + 10x + 2x + 20


= x (x + 10) + 2 (x + 10)


= (x + 10) (x + 2)


Hence, x3+13x2+32x+20 = (x + 1) (x + 10) (x + 2)


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