Answer:
The zeros are 4, -6, and 1.
Step-by-step explanation:
Given f(x) = x³ + x² - 26x + 24
(x - 4) is a factor of f(x). That means it is a zero of f(x).
To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).
That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]
[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]
Taking [tex]$ x^2 $[/tex] out, we have:
[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]
Taking (x - 4) common out, we have:
[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]
[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]
[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]
[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]
This means the zeros are 4, -6, & 1.
