Find the best solutions to your problems with the help of IDNLearn.com's expert users. Ask any question and receive timely, accurate responses from our dedicated community of experts.
Sagot :
To determine which monomials are factors of [tex]\(-100 x^6 y\)[/tex], we need to carefully examine the given monomials and see if they divide [tex]\(-100 x^6 y\)[/tex] evenly. Let us analyze each option step-by-step:
### Option A: [tex]\(-8 x^2\)[/tex]
1. Identify the variables and their exponents:
- [tex]\(-100 x^6 y\)[/tex] has [tex]\(x\)[/tex] with an exponent of 6 and [tex]\(y\)[/tex] with an exponent of 1.
- [tex]\(-8 x^2\)[/tex] has [tex]\(x\)[/tex] with an exponent of 2 and no [tex]\(y\)[/tex] component.
2. Compare the exponents of [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the candidate factor [tex]\(-8 x^2\)[/tex] is 2. This is less than the exponent of [tex]\(x\)[/tex] in [tex]\(-100 x^6 y\)[/tex] which is 6. This is good so far because 2 is a factor of 6.
3. Compare the constant coefficients:
- We need to check if [tex]\(-8\)[/tex] is a factor of [tex]\(-100\)[/tex].
- -100 divided by -8 does not result in an integer because [tex]\(100 / 8 = 12.5\)[/tex]; hence, -8 does not divide -100 evenly.
Since [tex]\(-8 x^2\)[/tex] does not divide [tex]\(-100 x^6 y\)[/tex] evenly due to the constant term, it is not a factor of [tex]\(-100 x^6 y\)[/tex].
### Option B: [tex]\(-4 x^3\)[/tex]
1. Identify the variables and their exponents:
- [tex]\(-100 x^6 y\)[/tex] has [tex]\(x\)[/tex] with an exponent of 6 and [tex]\(y\)[/tex] with an exponent of 1.
- [tex]\(-4 x^3\)[/tex] has [tex]\(x\)[/tex] with an exponent of 3 and no [tex]\(y\)[/tex] component.
2. Compare the exponents of [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the candidate factor [tex]\(-4 x^3\)[/tex] is 3. This is less than the exponent of [tex]\(x\)[/tex] in [tex]\(-100 x^6 y\)[/tex] which is 6. This is acceptable because 3 is a factor of 6.
3. Compare the constant coefficients:
- We need to check if [tex]\(-4\)[/tex] is a factor of [tex]\(-100\)[/tex].
- -100 divided by -4 equals 25, which is an integer. So, [tex]\(-4\)[/tex] divides [tex]\(-100\)[/tex] evenly.
4. Check for the [tex]\(y\)[/tex] variable:
- The candidate factor [tex]\(-4 x^3\)[/tex] does not include the [tex]\(y\)[/tex] variable, while [tex]\(-100 x^6 y\)[/tex] does have [tex]\(y\)[/tex] with an exponent of 1.
- Since the factor [tex]\(-4 x^3\)[/tex] lacks the [tex]\(y\)[/tex] term that is present in [tex]\(-100 x^6 y\)[/tex], it does not divide it completely.
Considering the [tex]\(y\)[/tex] component, [tex]\(-4 x^3\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
### Conclusion
Based on the above analysis:
- Option A: [tex]\(-8 x^2\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
- Option B: [tex]\(-4 x^3\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
Therefore, the correct answer is: C) None of the above.
### Option A: [tex]\(-8 x^2\)[/tex]
1. Identify the variables and their exponents:
- [tex]\(-100 x^6 y\)[/tex] has [tex]\(x\)[/tex] with an exponent of 6 and [tex]\(y\)[/tex] with an exponent of 1.
- [tex]\(-8 x^2\)[/tex] has [tex]\(x\)[/tex] with an exponent of 2 and no [tex]\(y\)[/tex] component.
2. Compare the exponents of [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the candidate factor [tex]\(-8 x^2\)[/tex] is 2. This is less than the exponent of [tex]\(x\)[/tex] in [tex]\(-100 x^6 y\)[/tex] which is 6. This is good so far because 2 is a factor of 6.
3. Compare the constant coefficients:
- We need to check if [tex]\(-8\)[/tex] is a factor of [tex]\(-100\)[/tex].
- -100 divided by -8 does not result in an integer because [tex]\(100 / 8 = 12.5\)[/tex]; hence, -8 does not divide -100 evenly.
Since [tex]\(-8 x^2\)[/tex] does not divide [tex]\(-100 x^6 y\)[/tex] evenly due to the constant term, it is not a factor of [tex]\(-100 x^6 y\)[/tex].
### Option B: [tex]\(-4 x^3\)[/tex]
1. Identify the variables and their exponents:
- [tex]\(-100 x^6 y\)[/tex] has [tex]\(x\)[/tex] with an exponent of 6 and [tex]\(y\)[/tex] with an exponent of 1.
- [tex]\(-4 x^3\)[/tex] has [tex]\(x\)[/tex] with an exponent of 3 and no [tex]\(y\)[/tex] component.
2. Compare the exponents of [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the candidate factor [tex]\(-4 x^3\)[/tex] is 3. This is less than the exponent of [tex]\(x\)[/tex] in [tex]\(-100 x^6 y\)[/tex] which is 6. This is acceptable because 3 is a factor of 6.
3. Compare the constant coefficients:
- We need to check if [tex]\(-4\)[/tex] is a factor of [tex]\(-100\)[/tex].
- -100 divided by -4 equals 25, which is an integer. So, [tex]\(-4\)[/tex] divides [tex]\(-100\)[/tex] evenly.
4. Check for the [tex]\(y\)[/tex] variable:
- The candidate factor [tex]\(-4 x^3\)[/tex] does not include the [tex]\(y\)[/tex] variable, while [tex]\(-100 x^6 y\)[/tex] does have [tex]\(y\)[/tex] with an exponent of 1.
- Since the factor [tex]\(-4 x^3\)[/tex] lacks the [tex]\(y\)[/tex] term that is present in [tex]\(-100 x^6 y\)[/tex], it does not divide it completely.
Considering the [tex]\(y\)[/tex] component, [tex]\(-4 x^3\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
### Conclusion
Based on the above analysis:
- Option A: [tex]\(-8 x^2\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
- Option B: [tex]\(-4 x^3\)[/tex] is not a factor of [tex]\(-100 x^6 y\)[/tex].
Therefore, the correct answer is: C) None of the above.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.
