ent 5 (Chapter 4 ) Suestion \( 2,4.4 .33 \) Part of 3 , Score: \( 1.74 \%, 0.8 \) of 46 points of these. \( 3 x^{3}-7 x \) Select the correct choice below and fill in the answer box to complete your choice. A. The polynomial cannot be simplible, and write it with descending powers. Then give the degree of the resulting polynomial, and tell whether it is a monomial, a binomial, a trinomial, or none B. The polynomial can be simplified. \( 3 x^{3}-7 x= \) The degree is is \( \square \). (Type a whole number.)

To tackle the polynomial \( 3x^{3} - 7x \), let’s first rewrite it in descending order, which is already done since the highest power of \( x \) appears first. To simplify this polynomial, we can factor out the common term \( x \): \( 3x^{3} - 7x = x(3x^{2} - 7) \). The degree of the resulting polynomial is \( 3 \), which is the highest exponent in the original expression. This is classified as a binomial since it consists of two terms: \( x \) and \( (3x^{2} - 7) \). Now, let's break down the concept a bit more! Did you know that polynomials can be classified based on the number of terms they contain? For instance, a polynomial with one term is called a monomial, while one with two terms is a binomial, and three terms make a trinomial. Another interesting aspect is factoring. When you factor a polynomial, you’re essentially simplifying it to make calculations easier or to find roots—values for \( x \) that make the polynomial equal to zero. Common mistakes include factoring incorrectly or forgetting to check for common factors at all! Always look for those hidden gems to make your life easier!