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].
