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

$\begin{gathered} (y^3+y^2)+(y+1)=y^2(\frac{y^3}{y^2}+\frac{y^2}{y^2})+(y+1) \\ (y^3+y^2)+(y+1)=y^2(y+1)+(y+1) \end{gathered}$

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

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

The factored form is

$(y+1)(y^2+1)$