Let's analyze the polynomial step-by-step.
Given polynomial:
[tex]\[ g(x) = -4x^3 - 5 \][/tex]
Step 1: Identify the polynomial type
To classify the polynomial, we need to look at the highest power of [tex]\( x \)[/tex]:
- The highest power of [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex], which means the polynomial is a cubic polynomial.
So, the correct classification is:
[tex]\[ \text{The polynomial is cubic.} \][/tex]
Step 2: Determine the leading term
The leading term of a polynomial is the term with the highest power of [tex]\( x \)[/tex]:
- Here, the term with the highest power of [tex]\( x \)[/tex] is [tex]\( -4x^3 \)[/tex].
So, the leading term is:
[tex]\[ -4x^3 \][/tex]
Step 3: Determine the leading coefficient
The leading coefficient is the coefficient of the leading term:
- For the leading term [tex]\( -4x^3 \)[/tex], the coefficient is [tex]\( -4 \)[/tex].
So, the leading coefficient is:
[tex]\[ -4 \][/tex]
Step 4: Determine the degree of the polynomial
The degree of a polynomial is the highest power of [tex]\( x \)[/tex] present in the polynomial:
- In this case, the highest power of [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex].
So, the degree of the polynomial is:
[tex]\[ 3 \][/tex]
Summary:
- The polynomial is cubic (Choice A).
- The leading term is [tex]\( -4x^3 \)[/tex].
- The leading coefficient is [tex]\( -4 \)[/tex].
- The degree of the polynomial is [tex]\( 3 \)[/tex].
Thus, the classification, leading term, leading coefficient, and degree of the polynomial [tex]\( g(x) = -4x^3 - 5 \)[/tex] are correctly identified as follows:
[tex]\[
(1, '-4x^3', -4, 3)
\][/tex]
