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 $(x+3)^2(x^2+9)$, which further simplifies to $(x+3)(x+3)(x-3i)(x+3i)$, matching option A.

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 $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } + 45 x + 54$