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Factor 9x^4-18x^3+36x^2

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Given the expression:


9x^4-18x^3+36x^2

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:


\begin{gathered} 9=3\cdot3 \\ 18=2\cdot3\cdot3 \\ 36=2\cdot2\cdot3\cdot3 \end{gathered}

Notice that all the coefficients have:


3\cdot3=9

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:


x^2

Hence:


GCF=9x^2

2. Now you can factor it out:


=9x^2(x^2-2x+4)

Hence, the answer is:


9x^2(x^2-2x+4)

User Mike Young
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