Question

Find the missing term in the expression and write them in decreasing order of exponents:

21m^7 - 7m^5 + 49m = 7m^(?)
A) 6
B) 4
C) 3
D) 2.

Answer 1

The missing term in the expression is found by factoring out 7m from each term, which gives us the highest remaining exponent of m, which is 6. Hence, the expression completes to 7m^(6), making the correct answer A) 6.

Step-by-step explanation:

To find the missing term in the expression 21m^7 - 7m^5 + 49m and have it match the form 7m^(?), we need to factor out a 7m from each term. Firstly, divide each term by 7m to see if the expression can be simplified.

Here is the step-by-step factoring:

1. Divide 21m^7 by 7m, which is 3m^(7-1) = 3m^6.
2. Divide -7m^5 by 7m, which is -m^(5-1) = -m^4.
3. Divide 49m by 7m, which is simply 7.

So after factoring out 7m, the resulting expression is 7m times (3m^6 - m^4 + 7). Since we only need to match the form 7m^(?), our missing exponent term is the largest exponent after factoring, which is 6. Therefore, the answer is A) 6.

We should also check if this answer is reasonable by confirming that there are no other terms that can be divided by 7m to give us a higher power of m, which there are not.