Question8. Determine the degree of $g(x) = x^2(x+3)(x+1)$

Studdy Solution

STEP 1

1. The degree of a polynomial is the highest power of $x$ when the polynomial is expanded.
2. Each factor contributes to the degree based on its own degree.
3. The degree of a product of polynomials is the sum of the degrees of the factors.

STEP 2

1. Identify the degree of each factor in the expression.
2. Sum the degrees of all factors to find the degree of $g(x)$ .

STEP 3

Identify the degree of each factor in the expression $g(x) = x^2(x+3)(x+1)$ .
- The factor $x^2$ has a degree of 2. - The factor $(x+3)$ is a linear polynomial, so it has a degree of 1. - The factor $(x+1)$ is also a linear polynomial, so it has a degree of 1.

STEP 4

Sum the degrees of all factors to find the degree of $g(x)$ .
- The total degree is the sum of the degrees of each factor: $ \text{Degree of } g(x) = 2 + 1 + 1 = 4 \]
The degree of the polynomial $g(x)$ is $\boxed{4}$ .

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