Question

Find the greatest common factor of 2(x-7) and 5(x-7)³.

a) 2(x-7)
b) 5(x-7)
c) 10(x-7)²
d) 5(x-7)²

Answer 1

The greatest common factor of 2(x-7) and 5(x-7)³ is 2(x-7), since it is the maximum shared factor between the two expressions.

Step-by-step explanation:

To find the greatest common factor (GCF) of 2(x-7) and 5(x-7)³, we must identify the largest expression that can divide both of the given terms. Here's how we figured it out:

• The GCF must contain the term (x-7) since it is present in both expressions.
• We can only take as many (x-7) terms as are in the expression with the fewest of them, so we're limited by 2(x-7), which has a single (x-7).
• The numeric part of the GCF has to be a factor of both 2 and 5 - the greatest such number is 1, since 2 and 5 are relatively prime.

So, the GCF does not include a numeric factor from both 2 and 5, but only the common algebraic factor. Therefore, the GCF is 2(x-7), which is option a.