Answer:
[tex]3x^{2}[/tex] is the greatest common factor of the polynomial.
Step-by-step explanation:
Given:
The polynomial is [tex]12x^{4} - 6x^{3} + 9x^{2}[/tex]
In order to determine the greatest common factor of all the terms, we find the greatest common factor of the coefficients separately and greatest common factor of the variables separately.
So, factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 6 = 1, 2, 3, 6
Factors of 9 = 1, 3, 9
Therefore, the greatest common factor among 12, 6, and 9 is 3.
Now, factors of [tex]x^{4}[/tex] = [tex]1, x, x^{2}, x^{3}, x^{4}[/tex]
Factors of [tex]x^{3}[/tex] = [tex]1, x, x^{2}, x^{3}[/tex]
Factors of [tex]x^{2}[/tex] = [tex]1, x, x^{2}[/tex]
Therefore, the greatest common factor among [tex]x^{4}, x^{3},x^{2}[/tex] is [tex]x^{2}[/tex].
Hence, the greatest common factor of all the terms of the polynomial is [tex]3x^{2}[/tex]
