College Algebra: How would you find the polynomial equation of the least possible degree with integer coefficients having a greatest common factor of 1 and whose roots include the numbers 0,4,-4?

Question

mathstudent55 · Answer

The polynomial with roots a, b, and c is:
(x - a)(x - b)(x - c) = 0

anonymous · Answer

It would just be (x-0)(x-4)(x+4)?

anonymous · Answer

And then factored together?

mathstudent55 · Answer

Yes to your first question. Set that equal to zero.
Then notice that x - 0 is simply x.
Multiply the other two binomials together using FOIL, and then multiply that result by x.

anonymous · Answer

Okay, I understand now, thank you very much! :)

anonymous · Answer

x^3-16?

mathstudent55 · Answer

You are welcome.

mathstudent55 · Answer

$x(x + 4)(x - 4) = 0$

$x(x^2 - 16) = 0$

$x^3 - 16x =0$

Don't forget to multiply x by the -16 term also.

anonymous · Answer

Oh, whoops, thank you again. :)

mathstudent55 · Answer

You're welcome.