Question

when the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x² the leading coefficient is 5, and the constant is 2. the leading coefficient is 2, and the constant is 5. the leading coefficient is -3, and the constant is 2. the leading coefficient is 2, and the constant is -3.

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. For a polynomial in one variable \(x\), the standard form is \(a_nx^n + a_{n - 1}x^{n-1}+\dots+a_1x + a_0\), where \(a_n\) is the leading coefficient (coefficient of the term with the highest degree) and \(a_0\) is the constant term.

Step2: Rewrite the given polynomial in standard form

The given polynomial is \(5x + 2-3x^2\). Rewriting it in descending order of exponents of \(x\), we get \(- 3x^2+5x + 2\).

Step3: Identify leading coefficient and constant term

In the standard form \(-3x^2 + 5x+2\), the term with the highest degree (degree 2) is \(-3x^2\), so the leading coefficient is \(-3\). The constant term (the term without \(x\)) is \(2\).

Answer:

The leading coefficient is \(-3\), and the constant is \(2\) (corresponding to the option: The leading coefficient is \(-3\), and the constant is 2).