Six statements about polynomials are given. Select all the statements that are true.(4 points)

Let's evaluate each statement about polynomials to determine which ones are true:

1. **\( 5a^2b−6ab^3c+3a^5 \) is a fifth degree polynomial.**
- The degree of a polynomial is determined by the term with the highest sum of exponents. In this case:
- \( 5a^2b \) has a degree of 3 (2 + 1 = 3)
- \( -6ab^3c \) has a degree of 5 (1 + 3 + 1 = 5)
- \( 3a^5 \) has a degree of 5.
- The highest degree is 5, so this statement is **true**.

2. **\( 12x - 10x^5 - 7 + 3x^4 \) has a leading coefficient of 12.**
- The leading coefficient is the coefficient of the term with the highest degree. The term with the highest degree is \( -10x^5 \), which has a leading coefficient of -10. Hence, this statement is **false**.

3. **\( 5a^2b−6ab^3c+3a^5 \) contains three terms.**
- The polynomial clearly has three distinct terms: \( 5a^2b \), \( -6ab^3c \), and \( 3a^5 \). Thus, this statement is **true**.

4. **\( 5a^2b−6ab^3c+3a^5 \) has a leading coefficient of 5.**
- The term with the highest degree is again \( -6ab^3c \) or \( 3a^5 \), and the leading coefficient is from one of these terms, not from \( 5a^2b \). Therefore, this statement is **false**.

5. **\( 12x−10x^5−7+3x^4 \) has a leading term of \( -10x^5 \).**
- The leading term, which is the term with the highest degree, is indeed \( -10x^5 \). So this statement is **true**.

6. **\( 12x−10x^5−7+3x^4 \) is equivalent to \( -10x^5 + 3x^4 + 12x - 7 \).**
- The expression is just reordered. Since polynomial terms can be written in any order, this statement is **true**.

In summary, the true statements are:

- \( 5a^2b−6ab^3c+3a^5 \) is a fifth degree polynomial.
- \( 5a^2b−6ab^3c+3a^5 \) contains three terms.
- \( 12x−10x^5−7+3x^4 \) has a leading term of \( -10x^5 \).
- \( 12x−10x^5−7+3x^4 \) is equivalent to \( -10x^5 + 3x^4 + 12x - 7 \).