Identify the greatest common factor of \( 12 x^{2} \) and \( 10 b^{3} x^{4} \)
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Mind Expander
To find the greatest common factor (GCF) of \( 12x^{2} \) and \( 10b^{3}x^{4} \), we first analyze the coefficients and the variables separately. The coefficients are 12 and 10, and the GCF of 12 and 10 is 2. Next, we look at the variable parts. The expression \( x^{2} \) indicates we have \( x \) raised to the power of 2 in the first factor, and \( x^{4} \) in the second. The GCF takes the variable with the lowest exponent, which is \( x^{2} \). Since the variable \( b \) doesn’t appear in both expressions, it is not included in the GCF. Thus, combining the GCF of the coefficients and the variable, we get: \[ \text{GCF} = 2x^{2} \]