Find all the zeros of the function and write the polynomial as a product of linear fac- tors.
$y ^ { 4 } - 16$
A) $\pm 2 ( y - 2 ) ( y + 2 )$
B) $\pm 2 , \pm 2 i ; ( y - 2 ) ( y - 2 ) ( y + 2 i ) ( y + 2 i )$
C) $\pm 2 , \pm 2 i ; ( y - 2 ) ( y + 2 ) ( y - 2 i ) ( y + 2 i )$
D) $\pm 2 i ; ( y - 2 i ) ( y + 2 i )$
E) $2,2 i ; ( y + 2 ) ( y + 2 ) ( y - 2 i ) ( y - 2 i )$

Question

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. 
$y ^ { 4 } - 16$ 
A) $\pm 2 ( y - 2 ) ( y + 2 )$
B) $\pm 2 , \pm 2 i ; ( y - 2 ) ( y - 2 ) ( y + 2 i ) ( y + 2 i )$
C) $\pm 2 , \pm 2 i ; ( y - 2 ) ( y + 2 ) ( y - 2 i ) ( y + 2 i )$
D) $\pm 2 i ; ( y - 2 i ) ( y + 2 i )$
E) $2,2 i ; ( y + 2 ) ( y + 2 ) ( y - 2 i ) ( y - 2 i )$

Quizplus · Accepted Answer

We can write the given polynomial as difference of squares $(y^2)^2-4^2 = (y^2-4)(y^2+4)$. Then, we continue to factorize as difference of squares: $(y^2-4) = (y-2)(y+2)$ and $(y^2+4) = (y-2i)(y+2i)$. Therefore, the zeros are $\pm 2$ and $\pm 2i$, and the polynomial can be written as $(y-2)(y+2)(y-2i)(y+2i)$. The correct choice is C.

Find All the Zeros of the Function and Write the Polynomial