Answer:
[tex](x-3)^3[/tex]
Step-by-step explanation:
Given polynomial:
[tex]x^3-9x^2+27x-27[/tex]
Given (x - 3) is a factor of the polynomial, divide the polynomial by the factor using long division to find the other factor:
[tex]\large \begin{array}{r}x^2-6x+9\phantom{)}\\x-3{\overline{\smash{\big)}\,x^3-9x^2+27x-27\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-3x^2)\phantom{-b0000000)}}\\-6x^2+27x-27\phantom{)}\\-~\phantom{()}\underline{(-6x^2+18x)\phantom{0000.}}\\9x-27\phantom{)}\\-~\phantom{()}\underline{(9x-27)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore:
[tex]x^3-9x^2+27x-27=(x-3)(x^2-6x+9)[/tex]
Factor (x² - 6x + 9):
[tex]\implies x^2-6x+9[/tex]
[tex]\implies x^2-3x-3x+9[/tex]
[tex]\implies x(x-3)-3(x-3)[/tex]
[tex]\implies (x-3)(x-3)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies x^3-9x^2+27x-27=(x-3)(x-3)(x-3)[/tex]
[tex]\implies x^3-9x^2+27x-27=(x-3)^3[/tex]
