What is the greatest common factor of the terms of the polynomial below 12x^4 - 6x^3 + 9x^2?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the polynomial:
12x^4 - 6x^3 + 9x^2
Find the greatest common factor.
Solution:
We first determine the greatest common factor of the numerical coefficients. The numerical coefficients are 12, 6 and 9, which is factorable by 3. Therefore their greatest common factor is 3. For the variable x, we can find the greatest common factor by looking at the lowest degree, or the variable x that has the lowest exponent, which in our case is x^2. Combining the two greatest common factor together, we'll have 3x^2.
12x^4 - 6x^3 + 9x^2
= 3x^2 ( 4x^2 - 2x + 3)
Final answer:
Greatest Common Factor: 3x^2