Assertion (A): `p(x)=14x^(3)-2x^(2)+8x^(4)+7x-3` is a polynomial of degree 3.
Reason (R):The highest power of x in the polynomial p(x) is the degree of the polynomial.

Options

A. Both A and R are true and R is the correct explanation for a
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true

Answer

To determine the truth of the assertion (A) and the reason (R), we will analyze the polynomial given in the assertion step by step.

### Step 1: Identify the polynomial
The polynomial given is:
\[ p(x) = 14x^3 - 2x^2 + 8x^4 + 7x - 3 \]

### Step 2: Determine the highest power of \( x \)
To find the degree of the polynomial, we need to identify the term with the highest power of \( x \). The terms in the polynomial are:
- \( 14x^3 \) (power 3)
- \( -2x^2 \) (power 2)
- \( 8x^4 \) (power 4)
- \( 7x \) (power 1)
- \( -3 \) (constant term, power 0)

Among these, the term with the highest power is \( 8x^4 \).

### Step 3: Conclude the degree of the polynomial
Since the highest power of \( x \) in the polynomial \( p(x) \) is 4 (from the term \( 8x^4 \)), we conclude that the degree of the polynomial is 4.

### Step 4: Evaluate the assertion (A)
Assertion (A) states that \( p(x) \) is a polynomial of degree 3. Since we found that the degree is actually 4, assertion (A) is **false**.

### Step 5: Evaluate the reason (R)
Reason (R) states that the highest power of \( x \) in the polynomial is the degree of the polynomial. This statement is indeed **true**, as the degree of a polynomial is defined as the highest power of \( x \) present in it.

### Final Conclusion
- Assertion (A) is false.
- Reason (R) is true.

Thus, the correct answer is that assertion (A) is false, but reason (R) is true.

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