Thread: Factoring 5th root polynomial

My question started with
Show -243 in polar form which I did, <243, ∏ >
Then find all fifth roots of -243, which I did
z0 = <3, ∏/5 >
z1
. . . .
z4 = <3, 9∏/5 >

Now I need to factorise the polynomial z^5 + 243 giving exact values of the real coeff's. in terms of sin, cos where appropriate.

I think it should be simple for me, but need a quick start as to what is being looked for.

Thank you for looking.

Originally Posted by froodles01

My question started with
Show -243 in polar form which I did, <243, ∏ >
Then find all fifth roots of -243, which I did
z0 = <3, ∏/5 >
z1
. . . .
z4 = <3, 9∏/5 >

Now I need to factorise the polynomial z^5 + 243 giving exact values of the real coeff's. in terms of sin, cos where appropriate.

I think it should be simple for me, but need a quick start as to what is being looked for.

Thank you for looking.

Well you already have all the fifth roots, though the arguments should be in the region .

So the factorisation of will be .