Answer:
B
Step-by-step explanation:
For a number to be a zero of the polynomial, the function has to be equal to 0 if we were to plug in the number into x.
Let's find each:
plugging in x = -2 into the function:
[tex]2(-2)^4-(-2)^3-42(-2)^2+16(-2)+160\\=0[/tex]
so this is a zero.
Plugging in x = 2 into the function:
[tex]2(2)^4-(2)^3-42(2)^2+16(2)+160\\=48[/tex]
This is NOT a zero
Plugging in x = 4 into the function:
[tex]2(4)^4-(4)^3-42(4)^2+16(4)+160\\=0[/tex]
this is a zero
Plugging in x = -4 into the function:
[tex]2(-4)^4-(-4)^3-42(-4)^2+16(-4)+160\\=0[/tex]
this is a zero
hence, x = 2 in NOT a zero, answer choice B is right
