Answer:
C. Bart evaluates 3x⁴ - 10x³ + 11x - 172, when x = 4. He determines that the value of the expression is 0, and concluded that x - 4 is a factor.
Step-by-step explanation:
According to the factor theorem, if f(4) = 0, then (x - 4) is a factor of f(x) = 3x⁴ - 10x³ + 11x - 172.
For Bart to proceed using this factor theorem, Bart should evaluate the expression when x = 4, as shown below:
f(x) = 3x⁴ - 10x³ + 11x - 172
Substitute the value of x
f(4) = 3(4)⁴ - 10(4)³ + 11(4) - 172
f(4) = 3(256) - 10(64) + 44 - 172
f(4) = 768 - 640 + 44 - 172 = 0.
Since f(x) = 0, then (x - 4) is a factor of 3x⁴ - 10x³ + 11x - 172.
Therefore, the answer is: "C. Bart evaluates 3x⁴ - 10x³ + 11x - 172, when x = 4. He determines that the value of the expression is 0, and concluded that x - 4 is a factor."
