Question

5 Let P be a polynomial function, and P(x) = x4 - dr³ + 8x² - 14x + 16.

PART A
If (x - 2) is a factor of the polynomial, what is the value of d?
V
PART B
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Answer 1

To find the value of d when (x - 2) is a factor of the polynomial, substitute x = 2 into the polynomial function and solve for d. The value of d is 6.

Step-by-step explanation:

To find the value of d when (x - 2) is a factor of the polynomial, we can use the Remainder Theorem. According to the theorem, if (x - 2) is a factor of P(x), then P(2) should be equal to 0. Therefore, substituting x = 2 into the polynomial function P(x) will give us the value of d:

P(2) = (2)^4 - d(2)^3 + 8(2)^2 - 14(2) + 16

Simplifying the expression:

P(2) = 16 - 8d + 32 - 28 + 16

P(2) = 48 - 8d

Since (x - 2) is a factor of P(x), P(2) = 0. Therefore, we can solve the equation:

48 - 8d = 0

Simplifying the equation further:

8d = 48

d = 48/8

d = 6

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