Question

Lena found the greatest common factor (GCF) of 24ab2c3 and 30a2b3c2 to be 6abc2 by using these steps:

Step 1: GCF of 24 and 30 is 6
Step 2: Highest shared power between a and a2 is a
Step 3: Highest shared power between b2 and b3 is b
Step 4: Highest shared power between c3 and c2 is c2

In which step did Lena make a MISTAKE?
A) Step 1
B) Step 2
C) Step 3
D) Step 4
E) Lena's work is correct.

Answer 1

The mistake in Lena's steps to find the Greatest Common Factor (GCF) was made in Step 3, where she incorrectly identified 'b' instead of 'b^2' as the highest shared power of b between the two expressions.

Step-by-step explanation:

The question asks about the step where Lena made a mistake in finding the Greatest Common Factor (GCF) of the given algebraic expressions 24ab2c3 and 30a2b3c2. Upon examining Lena's method, we can identify that she did not select the correct highest shared power of b in the expressions. Now, let's go through the steps individually:

• Step 1: Correct, the GCF of 24 and 30 is indeed 6.
• Step 2: Correct, the highest shared power of a in both expressions is a, because a is a1 and the exponent can't be higher than 1 in both terms if they are to have a common factor.
• Step 3: Incorrect, the highest shared power of b should be b2 since b2 can divide both b2 and b3 evenly.
• Step 4: Correct, the highest shared power of c indeed is c2.

Therefore, the GCF should be 6ab2c2, and the mistake was made in Step 3 where Lena should have identified b2 rather than b as the highest power of b that is common to both terms.

Answer 2

I believe the answer is B.