Bart uses the factor theorem to determine whether x-4 is a factor of 3x⁴- 10x³+11x-172. How does he proceed to the correct 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."

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step-by-step explanation: