Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$
A) $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$
B) $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$
C) $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$
D) $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$
E) $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$

Question

Quizplus · Accepted Answer

Given the zeros -4, -1, 0, 1, and 4, the polynomial can be constructed as $f(x) = (x + 4)(x + 1)x(x - 1)(x - 4)$. Multiplying these factors out, while ensuring the leading coefficient is one, results in $f(x) = x^5 - 17x^3 + 16x$, which matches option E.

Find a Fifth Degree Polynomial Function of the Lowest Degree −4,−1,0,1,4- 4 , - 1,0,1,4−4,−1,0,1,4

Find a Fifth Degree Polynomial Function of the Lowest Degree $- 4 , - 1,0,1,4$