Question

How to factorise the cubic polynomial y cube + 13 y square + 32 y + 20

Answer 1

Answer:

Step-by-sLet p (x) = y^3 + 13y^2 +32y + 20

Using hit and trial method

y= -1

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

=-33+ 33

= 0

So, (y +1 ) is a factor of p (y) [by factor theorem]

To fing other factors we must divide p (y) by (y+1)

And the other factor found is y^2 +12y + 10

Factorising y^2 +12y +20

= y^2 +10y + 2y +20

= y (y +10) +2 (y +10)

= (y+2)(y+10)

So, polynomial p (y) would be factorised as (y+2)(y +10)(y+1).

Answer 2

Step-by-step explanation:

y cube ➕ 13 square ➕ 12y ➕ 20y ➕ 20

y cube ➕ y square ➕ 12y square ➕ 12y ➕ 20y ➕ 20

y square(y ➕ 1) ➕ 12(y ➕ 1) ➕ 20(y ➕ 1)

(y ➕ 1) (y square ➕12y ➕ 20)