The value for p will be equal to 3 / 4.
We have the function as:
f(x) = (x - 1)³ + 6(p x + 4) 2
f(x) = x³ - 3 x² + 3 x - 1 + 12 p x + 48
f(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47
Now, it is divided by x + 2 and leaves a remainder -3.
This means that if we will subtract 3 from f(x), it will be perfectly divisible by x + 2.
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47 - 3
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 44
Now put x = -2:
(-2)³ - 3 (-2)² + 3 (-2) ( 1 + 4 p) + 44 = 0
-8 - 12 - 6 ( 1 + 4 p) + 44 = 0
- 20 - 6 - 24 p + 44 = 0
24 p = 18
p = 3 / 4.
Therefore, the value for p will be equal to 3 / 4.
Learn more about function here:
brainly.com/question/4025726
#SPJ9
