Question

find the zeros of the polynomial: f(x) = x³ - 3x² - x + 3 list your answers in ascending order. ?, ,

Explanation:

Step1: Group polynomial terms

$f(x) = (x^3 - 3x^2) + (-x + 3)$

Step2: Factor each group

$f(x) = x^2(x - 3) - 1(x - 3)$

Step3: Factor out common binomial

$f(x) = (x - 3)(x^2 - 1)$

Step4: Factor difference of squares

$f(x) = (x - 3)(x - 1)(x + 1)$

Step5: Set f(x)=0, solve for x

$x - 3 = 0 \implies x=3$; $x - 1 = 0 \implies x=1$; $x + 1 = 0 \implies x=-1$

Step6: Sort values ascending

$-1 < 1 < 3$

Answer:

$-1$, $1$, $3$