Question

Which of the following functions has a factor of x, minus, 6x−6? answer multiple choice answers

a)f(x)=x³ +9x² +14x−30
b)f(x)=x³ −3x² −22x 30
c)f(x)=x³ + 9x² -14x−24
d)f(x)=x³ −3x² −22x+ 24

Answer 1

To determine which function has a factor of x - 6x - 6, substitute x = 6 into each function and check which one gives us 0 as the result. The function f(x) = x³ - 3x² - 22x + 24 is the only one that satisfies this condition.

Step-by-step explanation:

To determine which of the given functions has a factor of x - 6x - 6, we need to check if any of the functions satisfy this condition.

Let's substitute x = 6 into each function and see which one gives us 0 as the result:

a) f(6) = 6³ + 9(6)² + 14(6) - 30 = 1296 + 324 + 84 - 30 = 1674, so this function does not have x - 6x - 6 as a factor.

b) f(6) = 6³ - 3(6)² - 22(6) + 30 = 216 - 108 - 132 + 30 = 6, so this function does not have x - 6x - 6 as a factor.

c) f(6) = 6³ + 9(6)² - 14(6) - 24 = 1296 + 324 - 84 - 24 = 1512, so this function does not have x - 6x - 6 as a factor.

d) f(6) = 6³ - 3(6)² - 22(6) + 24 = 216 - 108 - 132 + 24 = 0, so this function has x - 6x - 6 as a factor.

Therefore, the correct answer is d) f(x) = x³ - 3x² - 22x + 24.