Factor when dividing the function the remainder is zero. The factorized form of the function [tex]f(x)=-3x^2+6x-9[/tex] is -3(x²-2x+3).
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 second-order, we need to take the common terms out from the expression,
[tex]f(x)=-3x^2+6x-9[/tex]
Taking -3 as the common terms out of the entire function,
[tex]\begin{aligned}f(x)&=-3x^2+6x-9\\\\&=-3(x^2-2x+3)\end{aligned}[/tex]
Hence, the factorized function [tex]f(x)=-3x^2+6x-9[/tex] is -3(x²-2x+3).
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