Final answer:
To find the value of c, divide p(x) by (x³ - 4x² - cx + 33) and set the remainder equal to zero. Then solve the equation to determine the value of c.
Step-by-step explanation:
To find the value of c, we need to use the fact that (x³ - 4x² - cx + 33) is a factor of the polynomial p(x) = x³ - 4x² - cx + 33. This means that when we divide p(x) by (x³ - 4x² - cx + 33), the remainder should be zero. To determine the value of c, we can use polynomial long division or synthetic division.
Performing polynomial long division or synthetic division, we divide p(x) by (x³ - 4x² - cx + 33) and set the remainder equal to zero. Solving this equation will give us the value of c.
For example, if we find that the remainder is zero when we divide p(x) by (x³ - 4x² - cx + 33), then the value of c would be the constant term in the divisor.