Select from the following which is the polynomial of degree n that has the given zero(s).
Zero
Degree $x = 3$ $n = 3$

A) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$
B) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$
C) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$
D) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$
E) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$

Question

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zero
Degree $x = 3$ $n = 3$ ​
​
A) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$
B) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$
C) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$
D) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$
E) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$

Quizplus · Accepted Answer

A polynomial of degree 3 with a zero at $x = 3$ can be represented as $(x - 3)^3 = x^3 - 9x^2 + 27x - 27$, which matches option A.

Select from the Following Which Is the Polynomial of Degree x=3x = 3x=3

Select from the Following Which Is the Polynomial of Degree $x = 3$