Mathematics: Algebra 2 see the image below for my question!

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Algebra 2 see the image below for my question!

soleil26

15.01.2022

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

Step-by-step 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:

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

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