Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: -5, -3, 3; degree 3
A) $f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45$
B) $f ( x ) = x ^ { 3 } + 9 x - 5 x ^ { 2 } - 45$
C) $f ( x ) = x ^ { 3 } + 9 x + 5 x ^ { 2 } + 45$
D) $f ( x ) = x ^ { 3 } - 9 x + 5 x ^ { 2 } - 45$

Question

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: -5, -3, 3; degree 3 
A) $f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45$
B) $f ( x ) = x ^ { 3 } + 9 x - 5 x ^ { 2 } - 45$
C) $f ( x ) = x ^ { 3 } + 9 x + 5 x ^ { 2 } + 45$
D) $f ( x ) = x ^ { 3 } - 9 x + 5 x ^ { 2 } - 45$

Quizplus · Accepted Answer

The polynomial with zeros -5, -3, and 3 is $f(x) = (x + 5)(x + 3)(x - 3)$. Expanding this gives $f(x) = x^3 + 5x^2 - 9x - 45$, which matches option D.

Form a Polynomial Whose Zeros and Degree Are Given f(x)=x3−9x−5x2+45f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45f(x)=x3−9x−5x2+45

Form a Polynomial Whose Zeros and Degree Are Given $f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45$