Factor when dividing the function the remainder is zero. The factorized form of the function [tex]f(x)=-3x^3+12x^2[/tex] is -3x²(x-4).
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)=-3x^3+12x^2[/tex]
Taking -3x² as the common terms out of the entire function,
[tex]\begin{aligned}f(x)&=-3x^3+12x^2\\\\&=-3x^2(x-4)\end{aligned}[/tex]
Hence, the factorized function [tex]f(x)=-3x^3+12x^2[/tex] is -3x²(x-4).
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