Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: 3, multiplicity 2; -3, multiplicity 2; degree 4
A) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81$
B) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 18 x ^ { 2 } + 27 x - 81$
C) $f ( x ) = x ^ { 4 } + 18 x ^ { 2 } + 81$
D) $f ( x ) = x ^ { 4 } - 18 x ^ { 2 } + 81$

Question

Quizplus · Accepted Answer

Given zeros are 3 and -3, each with multiplicity 2, the polynomial can be formed as $(x-3)^2(x+3)^2$. Expanding this gives $x^4 - 18x^2 + 81$, which matches option D.

Form a Polynomial Whose Zeros and Degree Are Given f(x)=x4−6x3+18x2−27x+81f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81f(x)=x4−6x3+18x2−27x+81

Form a Polynomial Whose Zeros and Degree Are Given $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81$