Question

1.4 polynomial functions and rates of change
ap pre - calculus
find the leading coefficient and the degree of each polynomial.

1. (f(x)=-6x^{2}-6x - 3)

l.c. __ degree __

1. (f(x)=10x^{3}+7)

l.c. __ degree __

1. (f(x)=8x^{4}+3x^{3}-2x)

l.c. __ degree __

1. (f(x)=2x + 6x^{4})

l.c. __ degree __

Explanation:

1. For \(f(x)= - 6x^{2}-6x - 3\):

Step1: Identify leading - term

The leading - term of a polynomial is the term with the highest power of \(x\). For \(f(x)=-6x^{2}-6x - 3\), the leading - term is \(-6x^{2}\).

Step2: Determine leading coefficient and degree

The coefficient of the leading - term is the leading coefficient. So, the leading coefficient (L.C.) is \(-6\). The power of \(x\) in the leading - term is the degree of the polynomial, so the degree is \(2\).

1. For \(f(x)=10x^{3}+7\):

Step1: Identify leading - term

The leading - term of \(f(x)=10x^{3}+7\) is \(10x^{3}\).

Step2: Determine leading coefficient and degree

The leading coefficient (L.C.) is \(10\), and the degree is \(3\).

1. For \(f(x)=8x^{4}+3x^{3}-2x\):

Step1: Identify leading - term

The leading - term of \(f(x)=8x^{4}+3x^{3}-2x\) is \(8x^{4}\).

Step2: Determine leading coefficient and degree

The leading coefficient (L.C.) is \(8\), and the degree is \(4\).

1. For \(f(x)=2x + 6x^{4}\):

Step1: Identify leading - term

The leading - term of \(f(x)=2x + 6x^{4}\) is \(6x^{4}\).

Step2: Determine leading coefficient and degree

The leading coefficient (L.C.) is \(6\), and the degree is \(4\).

Answer:

1. L.C. \(-6\), Degree \(2\)
2. L.C. \(10\), Degree \(3\)
3. L.C. \(8\), Degree \(4\)
4. L.C. \(6\), Degree \(4\)