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When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?

[tex]\[5x + 2 - 3x^2\][/tex]

A. The leading coefficient is 5, and the constant is 2.
B. The leading coefficient is 2, and the constant is 5.
C. The leading coefficient is -3, and the constant is 2.
D. The leading coefficient is 2, and the constant is -3.

Sagot :

GinnyAnsweridn
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].
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