Let P be a polynomial function, and
P(x) = 23 – dx2 - 4x – 20. If
(2 – 2) is a factor of the polynomial, what is the value of
d?

The value of d = -5

The polynomial function   x³ +5 x² - 4x -20 =0

Step-by-step explanation:

Explanation

Given that the equation is third degree polynomial

p(x) = x³ - d x² - 4x -20

Given factors x= 2 and x=-2

Substitute 'x' = 2 in given polynomial

     8 -d(2²)-4(2) - 20 =0

⇒   8 - 4 d - 8 -20=0

⇒     - 4 d-20 = 0

⇒    - 4 d = 20

⇒         d = - 5

The value of d = -5

Verification:-

After substitution d =-5 in given polynomial

x³ - (-5) x² - 4x -20 =0

put x=2

8 +5(4)-8-20 =0

             20 =20

The factors are x= 2 and x=-2 of the given polynomial