Determine an equation in factored form for the Polynomial fu

Determine an equation in factored form for the Polynomial function represented.

Solution

This function has three x intercepts:

at x = 1, x = 2 and x = -1

therefore the given polynomial can be written as:

f(x) = (x + 1)(x - 2)(x - 1) + c

=> f(x) = (x - 1)(x² - x + 2) + c

=> f(x) = x³ - x² + 2x - x² + x - 2 + c

=> f(x) = x³ - 2x² + 3x + (c - 2 )

now y intercept for this function is : f(0) = 4

therefore (c - 2) = 4

=> c = 6

so the function is: f(x) = x³ - 2x² + 3x + 4.