Which of the following statementa is true of the polynomial x^2+6x^3-4+2x^5 A. The degree of the polynomial is 1. B. The leading coefficient of the polynomial is 1. C. The polynomial in standard form is 2x^5+6x^3+x^2-4 D. The polynomial is a trinomial.

To determine which statement is true about the polynomial \(x^{2}+6x^{3}-4+2x^{5}\), let's analyze each option:<br /><br />A. The degree of the polynomial is 1.<br />- The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power is 5, so the degree of the polynomial is 5, not 1. Therefore, this statement is false.<br /><br />B. The leading coefficient of the polynomial is 1.<br />- The leading coefficient is the coefficient of the term with the highest degree. In this polynomial, the term with the highest degree is \(2x^{5}\), and its coefficient is 2, not 1. Therefore, this statement is false.<br /><br />C. The polynomial in standard form is \(2x^{5}+6x^{3}+x^{2}-4\).<br />- To write a polynomial in standard form, we arrange the terms in descending order of their degrees. The given polynomial in standard form is \(2x^{5}+6x^{3}+x^{2}-4\), which matches the rearranged form. Therefore, this statement is true.<br /><br />D. The polynomial is a trinomial.<br />- A trinomial is a polynomial with three terms. The given polynomial has four terms: \(2x^{5}\), \(6x^{3}\), \(x^{2}\), and \(-4\). Therefore, this statement is false.<br /><br />Based on the analysis, the correct statement is:<br />C. The polynomial in standard form is \(2x^{5}+6x^{3}+x^{2}-4\).