Question

factorise x^3+13x^2+32x+20

Answer 1

Just check out for x= -1

It is a factor

So divide the polynomial by (x+1)

The result is x^2+12x+20

x= -2 , x = -10

So, x^3+13x^2+32x+20 = (x+1)(x+2)(x+10)

Answer 2

Heya friend,

Here's your answer,


The given question to be factorised is :-

x³ + 13x² + 32x + 20


p(x) = x³ + 13x² + 32x + 20


Let x = (-1)

We get,

p(–1)  = (–1)³ + 13(–1)² + 32(–1) + 20

p(-1)  = (–1) + 13 + (–32) + 20
       
p(-1)  =  12 + (-12)

p(-1) = 12-12 = 0


Therefore,


The factor of x³ + 13x² + 32x + 20 is (x+1)


On dividing , x³ + 13x² + 32x + 20  by (x+1)


We would obtain,


x² + 12x + 20


 Using split the term method, we split x² + 12x + 20



⇒ p(x) = x2 + 10x + 2x + 20
           = [x(x + 10) + 2(x + 10)]
           = (x + 10)(x + 2)


Adding up the factor of p(x) into it, we get


           = (x + 10)(x + 2)(x + 1)


Hence, the factors of  (x³ + 13x² + 32x + 20) are (x + 10)(x + 2)(x + 1)



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Thanks!!!


Hope this helps!!!




(Division is there in the attachment).