Question

Algebra 2

Please see the image below for my question!

Answer 1

`x=\pm i,x=-13`

Explanation:

Since
`x=-1` is a solution of
`x^4+14x^3+14x^2+14x+13`, by the factor theorem,
`(x+1)` is a factor.

We perform the long division as shown in the attachment to obtain:

`x^4+14x^3+14x^2+14x+13=(x+1)(x^3+13x+x+13)`

We now factor the cubic polynomial by grouping.

`x^4+14x^3+14x^2+14x+13=(x+1)(x^2(x+13)+1(x+13))`

`x^4+14x^3+14x^2+14x+13=(x+1)(x^2+1)(x+13)`

Hence the other roots are:

`x=\pm i,x=-13`