Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine which factors are part of the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex], we need to test each factor and see if it divides the polynomial without leaving a remainder. Here is a step-by-step explanation for each factor:
1. Factor: [tex]\( x^2 - 2 \)[/tex]
- To check if [tex]\( x^2 - 2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 - 2 \)[/tex].
- Result: [tex]\( x^2 - 2 \)[/tex] divides the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 - 2 \)[/tex] is a factor.
2. Factor: [tex]\( x + 1 \)[/tex]
- To check if [tex]\( x + 1 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x + 1 \)[/tex].
- Result: [tex]\( x + 1 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x + 1 \)[/tex] is not a factor.
3. Factor: [tex]\( x - 1 \)[/tex]
- To check if [tex]\( x - 1 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x - 1 \)[/tex].
- Result: [tex]\( x - 1 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x - 1 \)[/tex] is not a factor.
4. Factor: [tex]\( x^2 \)[/tex]
- To check if [tex]\( x^2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 \)[/tex].
- Result: [tex]\( x^2 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 \)[/tex] is not a factor.
5. Factor: [tex]\( x \)[/tex]
- To check if [tex]\( x \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x \)[/tex].
- Result: [tex]\( x \)[/tex] divides the polynomial without leaving a remainder.
- Conclusion: [tex]\( x \)[/tex] is a factor.
6. Factor: [tex]\( x^2 + 2 \)[/tex]
- To check if [tex]\( x^2 + 2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 + 2 \)[/tex].
- Result: [tex]\( x^2 + 2 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 + 2 \)[/tex] is not a factor.
Based on this analysis, the factors of the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] are:
- [tex]\( x^2 - 2 \)[/tex]
- [tex]\( x \)[/tex]
1. Factor: [tex]\( x^2 - 2 \)[/tex]
- To check if [tex]\( x^2 - 2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 - 2 \)[/tex].
- Result: [tex]\( x^2 - 2 \)[/tex] divides the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 - 2 \)[/tex] is a factor.
2. Factor: [tex]\( x + 1 \)[/tex]
- To check if [tex]\( x + 1 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x + 1 \)[/tex].
- Result: [tex]\( x + 1 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x + 1 \)[/tex] is not a factor.
3. Factor: [tex]\( x - 1 \)[/tex]
- To check if [tex]\( x - 1 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x - 1 \)[/tex].
- Result: [tex]\( x - 1 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x - 1 \)[/tex] is not a factor.
4. Factor: [tex]\( x^2 \)[/tex]
- To check if [tex]\( x^2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 \)[/tex].
- Result: [tex]\( x^2 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 \)[/tex] is not a factor.
5. Factor: [tex]\( x \)[/tex]
- To check if [tex]\( x \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x \)[/tex].
- Result: [tex]\( x \)[/tex] divides the polynomial without leaving a remainder.
- Conclusion: [tex]\( x \)[/tex] is a factor.
6. Factor: [tex]\( x^2 + 2 \)[/tex]
- To check if [tex]\( x^2 + 2 \)[/tex] is a factor, divide the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] by [tex]\( x^2 + 2 \)[/tex].
- Result: [tex]\( x^2 + 2 \)[/tex] does not divide the polynomial without leaving a remainder.
- Conclusion: [tex]\( x^2 + 2 \)[/tex] is not a factor.
Based on this analysis, the factors of the polynomial [tex]\( -12x^5 + 15x^3 + 18x \)[/tex] are:
- [tex]\( x^2 - 2 \)[/tex]
- [tex]\( x \)[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
