What is the first term of the product of (x 2 − 3x )( 5x 3 + x 5 − 6) when it is written in standard form?Question 2Select one:

To find the first term of the product of the polynomials $(x^2 - 3x)(5x^3 + x^5 - 6)$ when it is written in standard form, follow these steps:

1. Break Down the Problem

1. Identify the leading term of each polynomial.
2. Calculate the product of the leading terms.

2. Relevant Concepts

• The leading term of a polynomial is the term with the highest degree.
• To find the product of two polynomials, multiply their leading terms.

3. Analysis and Detail

1. For the first polynomial $x^2 - 3x$:

   • The leading term is $x^2$ (highest degree is 2).

2. For the second polynomial $5x^3 + x^5 - 6$:

   • The leading term is $x^5$ (highest degree is 5).

3. Now, we find the product of the leading terms: $(x^2)(x^5) = x^{2+5} = x^7$

4. Verify and Summarize

We have established that the leading term from $(x^2 - 3x)$ is $x^2$ and from $(5x^3 + x^5 - 6)$ is $x^5$. The product of these leading terms results in $x^7$, which verifies our calculation is correct.

Final Answer

The first term of the product when written in standard form is $x^7$.