Question

State the degree and leading coefficient of the polynomial function.
​f(x)equalsnegative 6left parenthesis x plus 3 right parenthesis squaredleft parenthesis x minus 3 right parenthesis squared
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Part 1
A.
​Degree: 4; leading​ coefficient: negative 6
B.
​Degree: 2; leading​ coefficient: 1
C.
​Degree: 2; leading​ coefficient: negative 6
D.
​Degree: 4; leading​ coefficient: 1

Answer 1

To determine the degree and leading coefficient of the polynomial function \( f(x) = -6(x + 3)^2(x - 3)^2 \), we first need to analyze the polynomial.

1. **Degree**:
- The term \( (x + 3)^2 \) has a degree of 2.
- The term \( (x - 3)^2 \) also has a degree of 2.
- The total degree of the polynomial is the sum of the degrees of these terms: \( 2 + 2 = 4 \).

2. **Leading Coefficient**:
- The leading coefficient is determined by the coefficient of the term with the highest degree when the polynomial is expanded.
- Since the polynomial is multiplied by \(-6\), the leading coefficient will be \(-6\).

Thus, the degree of the polynomial function is 4, and the leading coefficient is \(-6\).

The correct answer is:
**A. Degree: 4; leading coefficient: -6**.