Question

Use synthetic division to determine which of the given values is a zero of the function f(x)=3x² −11x+6.

Possible zeros: -3, 3, 6, 1

a) x=−3
b) x=3
c) x=6
d) x=1

Answer 1

To determine which of the given values is a zero of the function f(x) = 3x² −11x + 6 using synthetic division, substitute each value into the function and check if the result equals zero. The only value that yields zero is x = 3.

Step-by-step explanation:

To determine which of the given values is a zero of the function f(x) = 3x² −11x + 6 using synthetic division, we substitute each value into the function and check if the result is equal to zero. Let's check:

a) For x = -3: f(-3) = 3(-3)² −11(-3) + 6 = 27 + 33 + 6 = 66

b) For x = 3: f(3) = 3(3)² −11(3) + 6 = 27 - 33 + 6 = 0

c) For x = 6: f(6) = 3(6)² −11(6) + 6 = 108 - 66 + 6 = 48

d) For x = 1: f(1) = 3(1)² −11(1) + 6 = 3 - 11 + 6 = -2

From the above calculations, we can see that x = 3 is the only value that yields a result of zero when substituted into the function. Therefore, the answer is x = 3 (option b).