# How do you factor # z^3 + 7z + 7^2 + 7#?

##### 2 Answers

#### Answer:

It can be factored in two different ways. Check out the Explanation! :)

#### Explanation:

Apply the power function when it appears on a constant value:

We can now do two different factorings:

or

#### Answer:

#### Explanation:

I suspect the question has been mistranscribed somewhere along the line. A more plausible cubic that we can factor by grouping would be:

#z^3+7z+z^2+7 = (z^3+7x)+(z^2+7)#

#color(white)(z^3+7z+z^2+7) = z(z^2+7)+1(z^2+7)#

#color(white)(z^3+7z+z^2+7) = (z+1)(z^2+7)#

This can only be factored further using complex coefficients, since

#color(white)(z^3+7z+z^2+7) = (z+1)(z^2-(sqrt(7)i)^2)#

#color(white)(z^3+7z+z^2+7) = (z+1)(z-sqrt(7)i)(z+sqrt(7)i)#