Respuesta :
Remainder theorem can be used to check if a given number is root or not. The factors of the polynomial function given are: (x-2), (x+4), (x-6).
What is the remainder theorem for a polynomial?
When a polynomial f(x) is divided by (x-a), the remainder is f(a)
The given polynomial function is
[tex]f(x) = x^3 -4x^2 - 20x + 48[/tex]
One root is x = 6, thus, (x-6) is one of the factor (since, by remainder theorem the remainder of f(x)/(x-6) is f(6) which is 0 since x = 6 is a root. And for those divisions, who leave no remainder, are division by factors.)
Getting other two factors:
[tex]f(x) = x^3 -4x^2 - 20x + 48\\\\f(x) = x^3 -6x^2 + 2x^2 - 12x - 8x + 48\\\\f(x) = x^2(x-6) + 2x(x-6) - 8(x-6)\\\\f(x) = (x-6)(x^2 + 2x -8) = (x-6)(x^2 + 4x - 2x -8) = (x-6)(x(x+4)-2(x+4))\\\\f(x) = (x-6)(x+4)(x-2) = (x-2)(x+4)(x-6)[/tex]
Thus, the factors of the polynomial function given are: (x-2), (x+4), (x-6).
Learn more about polynomial reminder theorem here:
brainly.com/question/22081364
