Question

1. the only solution to the equation $(x - 4)(x - 10)=k$ is $x = 7$. what is the value of $k$?

a. $-14$
b. $-9$
c. $9$
d. $28$

1. if $x = -2$, what is the value of $6x^3 - x + 16$?

f. $-34$
g. $-30$
h. $62$
j. $66$

1. if $x = -4$, what is the value of $\frac{x^2 - 1}{x - 1}$?

a. $-\frac{17}{5}$
b. $-3$
c. $\frac{9}{5}$
d. $\frac{17}{5}$

Explanation:

Problem 1:

Step1: Substitute x=7 into equation

$(7-4)(7-10)=k$

Step2: Calculate each parenthesis

$(3)(-3)=k$

Step3: Compute final product

$k=-9$

Problem 2:

Step1: Substitute x=-2 into expression

$6(-2)^3 - (-2) + 16$

Step2: Calculate the cubic term

$6(-8) - (-2) + 16$

Step3: Perform multiplication and simplification

$-48 + 2 + 16$

Step4: Sum the values

$-30$

Problem 3:

Step1: Substitute x=-4 into expression

$\frac{(-4)^2 - 1}{-4 - 1}$

Step2: Compute numerator and denominator

$\frac{16 - 1}{-5}$

Step3: Simplify the fraction

$\frac{15}{-5}=-3$

Answer:

1. B. -9
2. G. -30
3. B. -3