Factor when dividing the function the remainder is zero. The factorized form of the function [tex]f(x)=x^3 -6x^2-5x+30[/tex] is (x²-5)(x-6).
A factor of a function is a factor which when multiplied by another the result is the function itself.
We know that in order to factorize a function of the third order, we need to take the common terms out from the expression,
[tex]f(x)=x^3 -6x^2-5x+30[/tex]
Taking x² as the common terms out of the first two terms, and -5 from the last two terms, therefore,
[tex]\begin{aligned}f(x)&=x^3 -6x^2-5x+30\\\\&=x^2(x-6)-5(x-6)\\\\&=(x^2-5)(x-6)\\\end{aligned}[/tex]
Hence, the factorized form of the function [tex]f(x)=x^3 -6x^2-5x+30[/tex] is (x²-5)(x-6).
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