To determine the leading coefficient and the constant of the polynomial [tex]\(5x + 2 - 3x^2\)[/tex], we first need to write the polynomial in standard form. The standard form of a polynomial arranges the terms in descending order of their degrees.
The given polynomial is [tex]\(5x + 2 - 3x^2\)[/tex]. Let's rearrange it in descending order based on the powers of [tex]\(x\)[/tex]:
[tex]\[ -3x^2 + 5x + 2 \][/tex]
Now that the polynomial is in standard form, we can identify the coefficients of each term:
- The leading term is the term with the highest degree, which is [tex]\(-3x^2\)[/tex]. The coefficient of this term is [tex]\(-3\)[/tex]. Therefore, the leading coefficient is [tex]\(-3\)[/tex].
- The constant term is the term with no [tex]\(x\)[/tex] (i.e., [tex]\(x^0\)[/tex]) and is [tex]\(2\)[/tex]. Thus, the constant is [tex]\(2\)[/tex].
Therefore, the values are:
- The leading coefficient is [tex]\(-3\)[/tex].
- The constant is [tex]\(2\)[/tex].
So the correct statement is: The leading coefficient is [tex]\(-3\)[/tex], and the constant is [tex]\(2\)[/tex].
