Question

Find a degree 4 polynomial having zeros -8, -1, 4 and 6 and the coefficient of x^4 equal 1.
The polynomial is

Answer 1

Well you know your zeroes. Therefore, they must satisfy:
(x+8)(x+1)(x-4)(x-6) = 0. That is the only way to obtain the zeroes.
After proper expansion, your result will be
x^4-x^3-58 x^2+136 x+192

Answer 2

so i'm just factoring?

Answer 3

i mean distibuting

Answer 4

The opposite. You know the factors already. (Generally, if x = a is a zero of polynomial, then (x-a) is one term of the polynomial.) Thus, you have to find the zeroes and multiply out.

Answer 5

Yes. Distributing.

Answer 6

thank you!

Answer 7

okay i've been working on this for a bit and I'm not getting the answer you did. I just want to make sure i'm distibuting right. so for
(x+8)(x+1)(x-4)(x-6)=0 did you take the x at the begininng of the equation and get x^4 or did you do x^2+x^2+x^2 and then for the 8 did you do 8x^3 or did you do 8x+8x+8x?

Answer 8

I usually just split the two up so (x+8)(x+1) and then (x-4)(x-6). Then you just have to distribute equations.

Answer 9

*distribute 2 equations

Answer 10

\[(x^2+9x+8)*(x^2-10x+24)\]

Answer 11

\[(x^4-10x^3+24x^2+9x^3-90x^2+216x+8x^2-80x+192)\]

Answer 12

thank you!