Respuesta :
f(x) = 3x³ + 3x² - 6x
given the factors of the polynomial , then
f(x) =ax(x - 1)(x + 2) ( a is a multiplier )
to find a use f(2) = 24
f(2) = 2a(1)(4) = 24 ⇒8a = 24 ⇒ a = 3, thus
f(x) = 3x(x² + x - 2) = 3x³ + 3x² - 6x
The polynomial function is [tex]f(x) = 3x^3 + 3x^2 - 6x[/tex].
Given that,
- f(2) = 24.
- And, x– 1, x and x+ 2 represents the factors of the polynomial.
Now based on the above information, the calculation is as follows:
f(x) =ax(x - 1)(x + 2)
Here a is a multiplier.
Now
f(2) = 24
f(2) = 2a(1)(4) = 24
8a = 24
a = 3
It can be write as
[tex]f(x) = 3x(x^2 + x - 2)[/tex]
[tex]f(x) = 3x^3 + 3x^2 - 6x[/tex].
Therefore we can conclude that the polynomial function is [tex]f(x) = 3x^3 + 3x^2 - 6x[/tex].
Learn more: brainly.com/question/12976257
