Question

Select all that apply.Which of the following are linear factors of p(x) = x3 - 2x2 - 5x + 6?Ox-1Ox+2Ox-3Ox+1

Answer 1

(x - 1), (x + 2) and (x- 3)

Explanations:

Given the polynomial functon

`P(x)=x^3-2x^2-5x+6`

Check if x = 1 is a solution;

`\begin{gathered} P(1)=1^3-2(1)^2-5(1)+6 \\ P(1)=1-2-5+6 \\ P(1)=0 \end{gathered}`

Since P(1) = 0, hence x - 1 is a factor

Divide the polynomial function by x - 1 as shown:

`(x^3-2x^2-5x+6)/(x-1)=x^2-x-6`

Factorize the resulting quadratic function

`\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}`

Hence the linear factors of the polynomial function are (x - 1), (x + 2) and (x- 3)