Question

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

Answer 1

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)`