Question

What are the zeros of the polynomial function?

f(x)=x^4+2x^3−16x^2−2x+15

Select each correct answer.

−5
−1
0
1
3
5

Answer 1

Answer:

-5, -1, 1, 3 ,5

Step-by-step explanation:

(x - 1)(x + 1)(x - 3)(x + 5) = x^4 + 2x^3 - 16x^2 - 2x + 15

The zeros are 1, -1, 3, and -5

−5    YES

−1     YES

0       NO

1       YES

3      YES

5      NO

Answer 2

Answer:

$\huge\boxed{\{-5,\ -1,\ 1,\ 3\}}$

Step-by-step explanation:

$f(x)=x^4+2x^3-16x^2-2x+15\\\\=x^4+2x^3-x^2-2x-15x^2+15\\\\=x^3(x+2)-x(x+2)-15(x^2-1)\\\\=(x+2)(x^3-x)-15(x^2-1)\\\\=(x+2)x(x^2-1)-15(x^2-1)\\\\=(x^2-1)\bigg[x(x+2)-15\bigg]\\\\=(x^2-1)(x^2+2x-15)\\\\=(x^2-1)(x^2+5x-3x-15)\\\\=(x^2-1)\bigg[x(x+5)-3(x+5)\bigg]\\\\=(x^2-1)(x+5)(x-3)\\\\=(x-1)(x+1)(x+5)(x-3)\\\\\bold{x=1\ \vee\ x=-1\ \vee\ x=-5\ \vee\ x=3}$