IDNLearn.com: Your go-to resource for finding precise and accurate answers. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.
Sagot :
To determine which polynomial is in standard form, we need to check whether the terms of the polynomial are arranged in descending order of their power of \(x\).
Given the polynomials:
1. \(12 x - 14 x^4 + 11 x^5\)
2. \(-6 x - 3 x^2 + 2\)
3. \(11 x^3 - 6 x^2 + 5 x\)
4. \(14 x^9 + 15 x^{12} + 17\)
Let's analyze each polynomial one by one:
1. \(12 x - 14 x^4 + 11 x^5\)
- Terms: \(12 x\), \(-14 x^4\), \(11 x^5\)
- Powers of \(x\): \(1, 4, 5\)
- The powers \(1, 4, 5\) are not in descending order. Hence, this polynomial is not in standard form.
2. \(-6 x - 3 x^2 + 2\)
- Terms: \(-6 x\), \(-3 x^2\), \(2\)
- Powers of \(x\): \(1, 2, 0\)
- The powers \(2, 1, 0\) are in descending order. Hence, this polynomial is in standard form.
3. \(11 x^3 - 6 x^2 + 5 x\)
- Terms: \(11 x^3\), \(-6 x^2\), \(5 x\)
- Powers of \(x\): \(3, 2, 1\)
- The powers \(3, 2, 1\) are in descending order. Hence, this polynomial is in standard form.
4. \(14 x^9 + 15 x^{12} + 17\)
- Terms: \(14 x^9\), \(15 x^{12}\), \(17\)
- Powers of \(x\): \(9, 12, 0\)
- The powers \(12, 9, 0\) are not in descending order. Hence, this polynomial is not in standard form.
After checking each polynomial, we find that polynomial [tex]\( \boxed{2} \)[/tex] is in standard form as its terms are arranged in descending order of the power of [tex]\(x\)[/tex].
Given the polynomials:
1. \(12 x - 14 x^4 + 11 x^5\)
2. \(-6 x - 3 x^2 + 2\)
3. \(11 x^3 - 6 x^2 + 5 x\)
4. \(14 x^9 + 15 x^{12} + 17\)
Let's analyze each polynomial one by one:
1. \(12 x - 14 x^4 + 11 x^5\)
- Terms: \(12 x\), \(-14 x^4\), \(11 x^5\)
- Powers of \(x\): \(1, 4, 5\)
- The powers \(1, 4, 5\) are not in descending order. Hence, this polynomial is not in standard form.
2. \(-6 x - 3 x^2 + 2\)
- Terms: \(-6 x\), \(-3 x^2\), \(2\)
- Powers of \(x\): \(1, 2, 0\)
- The powers \(2, 1, 0\) are in descending order. Hence, this polynomial is in standard form.
3. \(11 x^3 - 6 x^2 + 5 x\)
- Terms: \(11 x^3\), \(-6 x^2\), \(5 x\)
- Powers of \(x\): \(3, 2, 1\)
- The powers \(3, 2, 1\) are in descending order. Hence, this polynomial is in standard form.
4. \(14 x^9 + 15 x^{12} + 17\)
- Terms: \(14 x^9\), \(15 x^{12}\), \(17\)
- Powers of \(x\): \(9, 12, 0\)
- The powers \(12, 9, 0\) are not in descending order. Hence, this polynomial is not in standard form.
After checking each polynomial, we find that polynomial [tex]\( \boxed{2} \)[/tex] is in standard form as its terms are arranged in descending order of the power of [tex]\(x\)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.