Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine which polynomial is in standard form, we need to ensure that the terms in the polynomial are ordered by descending powers of [tex]\( x \)[/tex]. The highest power (degree) should be listed first, followed by the next highest, and so on, down to the lowest power (constant term, if present).
Let's analyze each polynomial step-by-step:
1. Polynomial: [tex]\( 12x - 14x^4 + 11x^5 \)[/tex]
- Terms: [tex]\( 12x \)[/tex], [tex]\( -14x^4 \)[/tex], [tex]\( 11x^5 \)[/tex]
- Degrees: 1, 4, 5
- Ordered: No (5 > 4 > 1, so it should be [tex]\( 11x^5 - 14x^4 + 12x \)[/tex])
2. Polynomial: [tex]\( -6x - 3x^2 + 2 \)[/tex]
- Terms: [tex]\( -6x \)[/tex], [tex]\( -3x^2 \)[/tex], [tex]\( 2 \)[/tex]
- Degrees: 1, 2, 0
- Ordered: No (2 > 1 > 0, so it should be [tex]\( -3x^2 - 6x + 2 \)[/tex])
3. Polynomial: [tex]\( 11x^3 - 6x^2 + 5x \)[/tex]
- Terms: [tex]\( 11x^3 \)[/tex], [tex]\( -6x^2 \)[/tex], [tex]\( 5x \)[/tex]
- Degrees: 3, 2, 1
- Ordered: Yes (3 > 2 > 1, so it is already in standard form)
4. Polynomial: [tex]\( 14x^9 + 15x^{12} + 17 \)[/tex]
- Terms: [tex]\( 14x^9 \)[/tex], [tex]\( 15x^{12} \)[/tex], [tex]\( 17 \)[/tex]
- Degrees: 9, 12, 0
- Ordered: No (12 > 9 > 0, so it should be [tex]\( 15x^{12} + 14x^9 + 17 \)[/tex])
From this analysis, we can see that only the polynomial [tex]\( 11x^3 - 6x^2 + 5x \)[/tex] is in standard form. Thus, the correct polynomial in standard form is:
[tex]\[ 11x^3 - 6x^2 + 5x \][/tex]
Let's analyze each polynomial step-by-step:
1. Polynomial: [tex]\( 12x - 14x^4 + 11x^5 \)[/tex]
- Terms: [tex]\( 12x \)[/tex], [tex]\( -14x^4 \)[/tex], [tex]\( 11x^5 \)[/tex]
- Degrees: 1, 4, 5
- Ordered: No (5 > 4 > 1, so it should be [tex]\( 11x^5 - 14x^4 + 12x \)[/tex])
2. Polynomial: [tex]\( -6x - 3x^2 + 2 \)[/tex]
- Terms: [tex]\( -6x \)[/tex], [tex]\( -3x^2 \)[/tex], [tex]\( 2 \)[/tex]
- Degrees: 1, 2, 0
- Ordered: No (2 > 1 > 0, so it should be [tex]\( -3x^2 - 6x + 2 \)[/tex])
3. Polynomial: [tex]\( 11x^3 - 6x^2 + 5x \)[/tex]
- Terms: [tex]\( 11x^3 \)[/tex], [tex]\( -6x^2 \)[/tex], [tex]\( 5x \)[/tex]
- Degrees: 3, 2, 1
- Ordered: Yes (3 > 2 > 1, so it is already in standard form)
4. Polynomial: [tex]\( 14x^9 + 15x^{12} + 17 \)[/tex]
- Terms: [tex]\( 14x^9 \)[/tex], [tex]\( 15x^{12} \)[/tex], [tex]\( 17 \)[/tex]
- Degrees: 9, 12, 0
- Ordered: No (12 > 9 > 0, so it should be [tex]\( 15x^{12} + 14x^9 + 17 \)[/tex])
From this analysis, we can see that only the polynomial [tex]\( 11x^3 - 6x^2 + 5x \)[/tex] is in standard form. Thus, the correct polynomial in standard form is:
[tex]\[ 11x^3 - 6x^2 + 5x \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.