Let's evaluate each statement one by one to determine which ones are true.
-
5a²b − 6ab³c + 3a⁵ contains three terms.
True. This expression consists of three distinct terms: \(5a^2b\), \(-6ab^3c\), and \(3a^5\). -
5a²b − 6ab³c + 3a⁵ is a fifth degree polynomial.
True. The degree of a polynomial is the highest total degree of its terms. The term \(3a^5\) has a degree of 5 (since \(5\) is the highest exponent of \(a\) in that term), while the other terms have lower degrees. Therefore, this polynomial is of degree 5. -
12x − 10x⁵ − 7 + 3x⁴ has a leading term of −10x⁵.
True. The leading term of a polynomial is the term with the highest degree. Here, \(-10x^5\) is indeed the term with the highest degree (5). -
12x − 10x⁵ − 7 + 3x⁴ is equivalent to −10x⁵ + 3x⁴ + 12x − 7.
True. The order of addition does not affect the equivalency of polynomial expressions. This statement is a reordering of the original polynomial and is therefore true. -
5a²b − 6ab³c + 3a⁵ has a leading coefficient of 5.
False. The leading term is \(3a^5\), so the leading coefficient is actually \(3\), not \(5\). -
12x − 10x⁵ − 7 + 3x⁴ has a leading coefficient of 12.
False. The leading term is \(-10x^5\), so the leading coefficient is \(-10\), not \(12\).
Thus, the true statements are:
- 5a²b − 6ab³c + 3a⁵ contains three terms.
- 5a²b − 6ab³c + 3a⁵ is a fifth degree polynomial.
- 12x − 10x⁵ − 7 + 3x⁴ has a leading term of −10x⁵.
- 12x − 10x⁵ − 7 + 3x⁴ is equivalent to −10x⁵ + 3x⁴ + 12x − 7.