Identify the GCF of 12a4b3 + 8a3b2. 4a3b2 2a3b 4a2b 8a3b2
Mathematics · High School · Thu Feb 04 2021
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Given the value:
12a^4b^3 + 8a^3b^2
Determine the greatest common factor.
Solution:
In order to determine the greatest common factor, we must simply look for the term which has the lowest value since we have two terms a and b. In our case we'll have a^3 and b^2. For the numerical coefficient, we must list the factors of 12 and 8 first.
Factors of 8:
1, 2, 4, and 8
Factors of 12:
1, 2, 3, 4, 6, and 12
It can be seen that the greatest common factor is 4.
Now we can multiply 4 and a^3b^2, resulting to 4a^3b^2.
= 4 a^3b^2
Factor out 4a^3b^2.
= 12a^4b^3 + 8a^3b^2
= 4a^3b^2 (3ab + 2)
Final answer:
Greatest Common Factor = 4a^3b^2