Degree of the polynomial `p(x)=(x+2)(x-2)` is

Options

A. `2`
B. `1`
C. `0`
D. `3`

Answer

To find the degree of the polynomial \( p(x) = (x + 2)(x - 2) \), we can follow these steps:

### Step 1: Expand the polynomial
We start by expanding the expression using the difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \).

Here, we can let \( a = x \) and \( b = 2 \):
\[ p(x) = (x + 2)(x - 2) = x^2 - 2^2 \]

### Step 2: Simplify the expression
Now, we simplify the expression:
\[ p(x) = x^2 - 4 \]

### Step 3: Identify the highest power of \( x \)
To find the degree of the polynomial, we need to identify the highest power of \( x \) in the polynomial \( p(x) = x^2 - 4 \).

In this polynomial, the terms are:
- \( x^2 \) (which has a power of 2)
- \( -4 \) (which can be considered as \( -4x^0 \), having a power of 0)

### Step 4: Determine the degree
The degree of a polynomial is defined as the highest power of \( x \) present in the polynomial. Here, the highest power is 2 (from the term \( x^2 \)).

Thus, the degree of the polynomial \( p(x) \) is:
\[ \text{Degree} = 2 \]

### Final Answer:
The degree of the polynomial \( p(x) = (x + 2)(x - 2) \) is **2**.

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