Answer
(x - 1), (x + 2) and (x- 3)
Explanations:
Given the polynomial functon
[tex]P(x)=x^3-2x^2-5x+6[/tex]
Check if x = 1 is a solution;
[tex]\begin{gathered} P(1)=1^3-2(1)^2-5(1)+6 \\ P(1)=1-2-5+6 \\ P(1)=0 \end{gathered}[/tex]
Since P(1) = 0, hence x - 1 is a factor
Divide the polynomial function by x - 1 as shown:
[tex]\frac{x^3-2x^2-5x+6}{x-1}=x^2-x-6[/tex]
Factorize the resulting quadratic function
[tex]\begin{gathered} x^2-x-6=x^2-3x+2x-6 \\ x^2-x-6=x(x-3)+2(x-3) \\ x^2-x-6=(x+2)(x-3) \end{gathered}[/tex]
Hence the linear factors of the polynomial function are (x - 1), (x + 2) and (x- 3)
