How do you factor z3+7z+72+7?

2 Answers
Júlio B.
Jun 13, 2017

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

Explanation:

Apply the power function when it appears on a constant value:
z3+7z+72+7=z3+7z+49+7=z3+7z+56.

We can now do two different factorings:

→ by z:
z(z2+7)+56

or

→ by 7:
z3+7(z+8)

George C.
Jul 21, 2017

z3+7z+z2+7=(z+1)(z2+7)

z3+7z+z2+7=(z+1)(z−√7i)(z+√7i)

Explanation:

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

z3+7z+z2+7=(z3+7x)+(z2+7)

z3+7z+z2+7=z(z2+7)+1(z2+7)

z3+7z+z2+7=(z+1)(z2+7)

This can only be factored further using complex coefficients, since z2+7>0 for any real values of z ...

z3+7z+z2+7=(z+1)(z2−(√7i)2)

z3+7z+z2+7=(z+1)(z−√7i)(z+√7i)

Related questions
See all questions in Factoring Completely
Impact of this question
1649 views around the world
You can reuse this answer
Creative Commons License