Question

Let P be a polynomial function, and P(x) = x - dx³ + 11x² - 18x + 24. If

(x - 1) is a factor of the polynomial, what is the value of d? Explain or show how
you know.
x-14-d (x-1)³ +11 (x-1)²-18 (x+1)+2

Answer 1

To find the value of d, substitute x = 1 into the polynomial and equate it to zero. The value of d is 18.

Step-by-step explanation:

To determine the value of d, we can use the fact that (x - 1) is a factor of the polynomial. This means that when we substitute x = 1 into the polynomial, the result should be zero.

Let's substitute x = 1 into the polynomial:

P(1) = 1 - d(1)³ + 11(1)² - 18(1) + 24 = 1 - d + 11 - 18 + 24 = 18 - d

Since (x - 1) is a factor, P(1) = 0, so 18 - d = 0. Solving this equation, we find that d = 18.

Learn more about Finding the value of d when a polynomial has a factor