Let's solve the problem step by step to find the values of the leading coefficient and the constant for the polynomial [tex]\( 5x + 2 - 3x^2 \)[/tex].
1. Write the polynomial in standard form:
The standard form of a polynomial orders its terms by the descending powers of [tex]\( x \)[/tex]. This means that the term with the highest exponent is written first, followed by terms with lower exponents.
So, for the polynomial [tex]\( 5x + 2 - 3x^2 \)[/tex]:
[tex]\[ -3x^2 + 5x + 2 \][/tex]
2. Identify the leading coefficient:
The leading coefficient is the coefficient of the term with the highest power of [tex]\( x \)[/tex]. In this case, the term with the highest power of [tex]\( x \)[/tex] is [tex]\( -3x^2 \)[/tex]. Therefore, the leading coefficient is [tex]\( -3 \)[/tex].
3. Identify the constant term:
The constant term is the term without any [tex]\( x \)[/tex] variable. In this polynomial, the constant term is [tex]\( 2 \)[/tex].
To summarize:
- The leading coefficient is [tex]\( -3 \)[/tex].
- The constant term is [tex]\( 2 \)[/tex].
Thus, the correct answer is:
The leading coefficient is [tex]\( -3 \)[/tex], and the constant is [tex]\( 2 \)[/tex].
