Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } + 45 x + 54$$
A) $f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 3 i ) ( x + 3 i )$
B) $f ( x ) = ( x - 3 ) ( x + 2 ) ( x - 3 ) ( x + 3 )$
C) $f ( x ) = ( x - 1 ) ( x - 6 ) ( x - 3 i ) ( x + 3 i )$
D) $f ( x ) = ( x - i \sqrt { 6 } ) ( x + i \sqrt { 6 } ) ( x - 3 ) ( x + 3 )$

Question

Quizplus · Accepted Answer

The zeros of the polynomial can be found by factoring or using synthetic division. The given polynomial $f(x) = x^4 + 5x^3 + 15x^2 + 45x + 54$ can be factored into $(x + 3)(x + 2)(x^2 + 9)$, where $x^2 + 9$ further factors into $(x - 3i)(x + 3i)$, giving the linear factors as $(x + 3)(x + 2)(x - 3i)(x + 3i)$.

Find All Zeros of the Function and Write the Polynomial f(x)=x4+5x3+15x2+45x+54f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } + 45 x + 54f(x)=x4+5x3+15x2+45x+54

Find All Zeros of the Function and Write the Polynomial $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } + 45 x + 54$