Determine what value(s), if any, of the variable must be excluded.

Question

27z^3-64/3z-4

this problem has me crying I don't understand

Answer 1

(27z³-64)/(3z-4)

In math, division by 0 is undefined. So in rational expressions like this one, any value of z that makes the denominator equal to zero is excluded from the domain. So all you have to do is set the denominator to 0 and solve for z:

3z - 4 = 0

3z = 4

z = 4/3

So the value z = 4/3 is excluded from the expression's domain. The expression can be simplified as follows:

(27z³-64)/(3z-4)

((3x)³-4³)/(3z-4)

Apply the "difference of cubes" factoring formula to the numerator:

(3z-4)(9z²+12z+16)/(3z-4) = 9z² + 12z + 16 (which doesn't factor)

So when the expression is simplified, the 3z-4 in the denominator goes away. However, you have to find the exclusions to the domain before you simplify, so z = 4/3 is still excluded.