Given the expression:
[tex]9x^4-18x^3+36x^2[/tex]You can factor it by following these steps:
1. Find the Greatest Common Factors (GCF) of the terms:
- The Greatest Common Factor (GCF) of the coefficients can be found by decomposing each coefficient into their Prime Factors:
[tex]\begin{gathered} 9=3\cdot3 \\ 18=2\cdot3\cdot3 \\ 36=2\cdot2\cdot3\cdot3 \end{gathered}[/tex]Notice that all the coefficients have:
[tex]3\cdot3=9[/tex]Therefore, that is the Greatest Common Factor (GCF) of the coefficients.
- The Greatest Common Factor (GCF) of the variables is the variable with the lowest exponent:
[tex]x^2[/tex]Hence:
[tex]GCF=9x^2[/tex]2. Now you can factor it out:
[tex]=9x^2(x^2-2x+4)[/tex]Hence, the answer is:
[tex]9x^2(x^2-2x+4)[/tex]