Question

I know the answer is there but I want a explanation

Answer 1

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 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)

Answer 2

Have a look from first step
ther we have a question..Now we have to put some value to get 0.we have -1 as a factor ..so,now we have to find zero of -1 we get +1.
so after getting +1 as a factor divide it with the given question..
Then the solution you get by dividing ,do middle term splitting of it.
then you will get required factor.