The correct answer is letter S
We have by the intermediate value theorem that if a continuous function takes values both above and below zero at 2 points, there is a zero of the function in-between. We have that polynomials are continues. Let's calculate f(-6) and f(-5). f(-6)=-36 while f(-5)=-1. Thus, we cannot conclude that there is a root between them.
F(-2)=8, f(-1)=-1, so there is a flip; a zero must exist between them.
F(1)=-1, f(2)=20, so again there is a change of signs.
f(-5)=-1, f(-4)=14 so there is a root still.
We have that the only choice that does not have a root between the integers is choice a.
Option C: 
is the product of the rational expression.
Explanation:
The given rational expression is 
We need to determine the product of the rational expression.
<u>Product of the rational expression:</u>
Let us multiply the rational expression to determine the product of the rational expression.
Thus, we have;
Let us use the identity 
in the above expression.
Thus, we get;
Simplifying the terms, we get;
Thus, the product of the rational expression is
Hence, Option C is the correct answer.
Slot method
8 optionns n 1st slot
7 options in 2nd slot (since 1 is at 1st slot)
6 options in 3rd slot
5 options in 4th slot
8*7*6*5=1680 ways
Multiply everything in the parenthesis by a.
ac + ab = d
Subtract ab from both sides.
ac = d - ab
Divide a on both sides.
c = d - ab / a
Hope this helps!
