Answer:
[tex](x - 1)(x - 12)(x - 10)[/tex]
Step-by-step explanation:
Given
Factorize:
[tex]x^3 - 23x^2 + 142x - 120[/tex]
Required
Factorize
We start by checking for the factors of the given polynomial;
Check x - 1 = 0;
This implies that x = 1
Substitute 1 for x in [tex]x^3 - 23x^2 + 142x - 120[/tex]
[tex](1)^3 - 23(1)^2 + 142(1) - 120[/tex]
[tex]= 1 - 23 + 142 - 120[/tex]
[tex]= 0[/tex]
Since the result is 0, then x - 1 = 0 is a factor
Divide the polynomial by x - 1
(See attachment for long division)
The result is: [tex]x^2 - 22x + 120[/tex]
Hence, the factor is
[tex](x - 1)(x^2 - 22x + 120)[/tex]
Expand the quadratic function
[tex](x - 1)(x^2 - 12x - 10x + 120)[/tex]
Factorize
[tex](x - 1)(x(x - 12) - 10(x - 12))[/tex]
[tex](x - 1)(x - 12)(x - 10)[/tex]
Hence;
Factorizing [tex]x^3 - 23x^2 + 142x - 120[/tex] gives [tex](x - 1)(x - 12)(x - 10)[/tex]
