Degree of the polynomial `p(x)=3x^(4)+6x+7` is

Options

A. `4`
B. `5`
C. `3`
D. `1`

Answer

To find the degree of the polynomial \( p(x) = 3x^4 + 6x + 7 \), we can follow these steps:

### Step 1: Identify the polynomial
We start with the polynomial given:
\[ p(x) = 3x^4 + 6x + 7 \]

### Step 2: Determine the powers of \( x \)
Next, we identify the powers of \( x \) in each term of the polynomial:
- The first term \( 3x^4 \) has a power of \( 4 \).
- The second term \( 6x \) has a power of \( 1 \).
- The third term \( 7 \) can be considered as \( 7x^0 \), which has a power of \( 0 \).

### Step 3: Compare the powers
Now, we compare the powers of \( x \) from each term:
- The powers are \( 4 \) (from \( 3x^4 \)), \( 1 \) (from \( 6x \)), and \( 0 \) (from \( 7 \)).

### Step 4: Identify the highest power
The highest power among these is \( 4 \).

### Step 5: State the degree of the polynomial
Thus, the degree of the polynomial \( p(x) \) is:
\[ \text{Degree of } p(x) = 4 \]

### Final Answer
The degree of the polynomial \( p(x) = 3x^4 + 6x + 7 \) is \( 4 \).

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