Question

algebra 2 362403-6 fy - 1
benchmark test 2
what is the remainder when $4x^2 - 6x - 4$ is divided by $2x - 8$?
a. $\frac{2}{5}$
b. 36
c. $-\frac{3}{5}$
d. 2

Explanation:

Step1: Find root of divisor

Set $2x - 8 = 0$, solve for $x$:
$2x = 8 \implies x = 4$

Step2: Apply Remainder Theorem

Substitute $x=4$ into $4x^2 - 6x - 4$:
$$4(4)^2 - 6(4) - 4$$

Step3: Calculate the value

$$4(16) - 24 - 4 = 64 - 24 - 4 = 36$$

Answer:

B. 36