Question

Find the factors of y^3 + y^2 + y + 1

Answer 1

The given expression is

`y^3+y^2+y+1`

We will use the grouping to factor it

`y^3+y^2+y+1=(y^3+y^2)+(y+1)`

Take y^2 as a common factor from the first bracket

`\begin{gathered} (y^3+y^2)+(y+1)=y^2((y^3)/(y^2)+(y^2)/(y^2))+(y+1) \\ (y^3+y^2)+(y+1)=y^2(y+1)+(y+1) \end{gathered}`

Take the bracket (y + 1) as a common factor

`\begin{gathered} y^2(y+1)+(y+1)=(y+1)\lbrack(y^2(y+1))/((y+1))+((y+1))/((y+1))\rbrack \\ y^2(y+1)+(y+1)=(y+1)\lbrack y^2+1\rbrack \end{gathered}`

The factored form is

`(y+1)(y^2+1)`