Question

What polynomial has roots of -4, 2, and 5

Answer 1

If you have a polynomial with roots \(r_1, r_2,...r_n\) you can write it as a product of factors \(k(x-r_1)(x-r_2)...(x-r_n)\) where \(k\) is a constant.

Answer 2

To figure this out, we multiply out (x-a) where a is a root, and do this for all the roots. So:
\[(x+4)(x-2)(x-5)\] Will give us our polynomial. Try multiplying this out on your own and let me know if you'd like some help with it.

Answer 3

If those are your roots then your binomials will be the opposites. So (x+4)(x-2)(x-5) and you FOIL the last two and then (x+4) times that polynomial.

Answer 4

x3 - x2 - 22x + 40
x3 + x2 - 22x - 40
x3 + 3x2 - 18x - 40
x3 - 3x2 - 18x + 40

Answer 5

@JJenk Try multiplying out the factors on your own, it will give you good practice for similar questions.

Answer 6

We told you the steps. I have the answer. Work it out and tell me an answer :')

Answer 7

i got x3 - 3x2 - 18x + 40

Answer 8

Yes

Answer 9

Good job :)

Answer 10

the polynomial you obtained is but 1 of infinitely many polynomials with the identical set of roots. multiply your polynomial by any number except 0 and you get a different polynomial with the same roots.