Question

factorise it : x³+13x²+32x+20

Answer 1

hola!

Given poly. :- x³ + 13x² + 32x + 20

Let p(x) = x³ + 13x² + 32x + 20

Put x = –1 in p(x), we get

p(–1) = (–1)³ + 13(–1)² + 32(–1) + 20
        
= (–1) + 13 + (–32) + 20
        
= 33 – 33 = 0

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

Now divide p(x) with (x + 1), we get x² + 12x + 20

∴ p(x) = (x + 1)(x² + 12x + 20)

Let's now factorize:- x² + 12x + 20

⇒ p(x) = (x + 1)(x² + 10x + 2x + 20)
          
= (x + 1)[x(x + 10) + 2(x + 10)]
           
= (x + 1)(x + 10)(x + 2)

Hope it helps! :)