f(x) as a product of linear factors is determined as f(x) = (x + 1)(x² - 6x + 4).
How to calculate the linear factor of the polynomial?
The factors of the polynomial is calculated as follows;
The given polynomial function;
f(x) = x³ - 5x² - 2x + 4
The zero of the polynomial function is - 1, so a factor of the polynomial becomes;
x = - 1
x + 1 = 0
factor = (x + 1)
The other factors of the polynomial is calculated as follows;
x² - 6x + 4
---------------------------------
x + 1 | (x³ - 5x² - 2x + 4)
- (x³ + x²)
--------------------------------
-6x² - 2x + 4
- (-6x² - 6x)
-----------------------------------
4x + 4
- (4x + 4)
----------------------------
0
We cannot factorize the quotient (x² - 6x + 4) further, so the linear factor of the polynomial becomes;
f(x) = (x + 1)(x² - 6x + 4)