Which of the following is a factor of f(x) = 4x³ + 11x² - 75x + 18?
(x - 3), (x + 3), (x - 1/3), (x + 1/3)

Solution:

The factor of the polynomial f(x) is a term like (x - k) and only if f(k) = 0.

Let us test this condition for all the options given in the question.

To determine the factor we can proceed by considering the given options.

Given: Polynomial f(x) = 4x³ + 11x² - 75x + 18

From option (x - 3),

f(3) = 4(3)³ + 11(3)² - 75(3) + 18

f(3) = 4(27) + 11(9) - 75(3) + 18

f(3) = 108 + 99 - 225 + 18

f(3) = 225 - 225

f(3) = 0

Condition is satisfied.

From option (x + 3)

f(-3) = 4(-3)³ + 11(-3)² - 75(-3) + 18

f(-3) = 4(-27) + 11(9) - 75(-3) + 18

f(-3) = -108 + 99 + 225 + 18

f(-3) = 342 - 108

f(-3) = 252

f(-3) ≠ 0

Condition is not satisfied.

Therefore, (x - 3) is the factor of f(x) = 4x³ + 11x² - 75x + 18.

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Which of the following is a factor of f(x) = 4x³ + 11x² - 75x + 18?

Summary:

The factor of f(x) = 4x³ + 11x² - 75x + 18 is (x - 3). The factor of the polynomial f(x) is a term like (x - k) and only if f(k) = 0.