Question

question 3 of 10, step 2 of 2
consider the following rational expression.
(\frac{3z^2 - 19z - 14}{z^2 - 15z + 56})
step 2 of 2: determine what value(s), if any, of the variable must be excluded.
answer
select the number of values that must be excluded.
selecting an option will display any text boxes needed to complete your answer.
0
1
2
3

Explanation:

Step1: Set denominator equal to 0

$z^2 - 15z + 56 = 0$

Step2: Factor the quadratic equation

$(z-7)(z-8) = 0$

Step3: Solve for z values

$z-7=0 \implies z=7$; $z-8=0 \implies z=8$

Step4: Count excluded values

There are 2 excluded values.

Answer:

2 (Option: ○ 2)
The excluded values of $z$ are $7$ and $8$.