Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.
$- 3 , - 1,0,1,3$
A) $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } - 32 x ^ { 2 } + 48 x$
B) $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } + 32 x ^ { 2 } + 48 x$
C) $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 3 x ^ { 2 } + 12 x$
D) $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$
E) $f ( x ) = x ^ { 5 } - 10 x ^ { 3 } + 9 x$

Question

Quizplus · Accepted Answer

Given the zeros $-3, -1, 0, 1, 3$, the polynomial can be constructed as $f(x) = (x + 3)(x + 1)x(x - 1)(x - 3)$. When multiplied out, this simplifies to $f(x) = x^5 - 10x^3 + 9x$, which matches option E.

Find a Fifth Degree Polynomial Function of the Lowest Degree −3,−1,0,1,3- 3 , - 1,0,1,3−3,−1,0,1,3

Find a Fifth Degree Polynomial Function of the Lowest Degree $- 3 , - 1,0,1,3$