Question

Find a polynomial of degree n that has the given zeros. (There are many correct answers.)
zeros: -3,1,3,7
degree: n=5
i do not know how to correctly expand

Answer 1

you have 4 zeros; so that makes at least a 4 degree poly.

one of them has to be doubled right?

Answer 2

the -3 and 3 create a difference of squares:
(x+3)(x-3) = x^2-9 for starters

Answer 3

(x-1)^2 will take care of the double zero and we get:

(x^2 -2x +1)(x^2-9)(x-7) so far

Answer 4

now just multiply them out...

Answer 5

x^2 -2x +1
x^2-9
-------------
x^4 -2x^3 +x^2
-9x^2+18x-9
----------------------
x^4 -2x^3-8x^2+18x-9
x -7
----------
x^5 -2x^4 -8x^3 +8x^2 -9x
-7x^4 +14x^3+56x^2-126x+63
---------------------------------
x^5 -9x^4 +6x^3 +64x^2 -135x +63

maybe

Answer 6

i see a typo that messed me up:

x^5 -2x^4 -8x^3 +18x^2 -9x
-7x^4 +14x^3+56x^2-126x+63
---------------------------------
x^5 -9x^4 +6x^3 +74x^2 -135x +63

thats better