Polynomials

To solve the problem, we need to evaluate the product of the given polynomials at .

1. Understand the Problem:
We are given the product of two polynomials and , and we are asked to find the value of , where:

2. Simplify the Expression:
We can simplify the product of the polynomials using the formula , where and :

3. Apply the Factorization:
Thus, we have:
Now, substitute into the expression:

Final Answer:
The correct answer is option (A): 0.

To solve the problem, we need to find the degree of the polynomial:

1. Understanding the Degree of a Polynomial:
The degree of a polynomial is the highest power (exponent) of the variable in the expression.

2. Analyzing Each Term:

- : Degree = 6

- : Degree = 4

- : Degree = 2

- : Constant term, Degree = 0

3. Identifying the Highest Degree:
Among all terms, the highest power of is 6.

Final Answer:
The degree of the polynomial is 6 (Option C).

To solve the problem, we need to find the zeros (roots) of the quadratic polynomial:

1. Express the Polynomial in Standard Form:
The expression is already in standard form:

2. Factoring the Expression:
Factor out the common term :

3. Applying the Zero Product Property:
Set each factor equal to zero:

Final Answer:
The zeros of the polynomial are

To solve the problem, we need to form a quadratic polynomial given the sum and product of its zeroes.

1. General Form of Quadratic Polynomial:
The quadratic polynomial with sum of roots and product of roots is given by:

2. Given:
Sum of zeroes = 1, Product of zeroes = 1

3. Substituting Values:

Final Answer:
The corresponding quadratic polynomial is .

Step 1: Identify the given polynomial.

The given polynomial is .

Step 2: Recognize the standard form of a quadratic polynomial.

The general form is:

Comparing: , ,

Step 3: Use the formula for product of zeroes of a quadratic polynomial.

The formula is:

Step 4: Substitute the values.

So, the product of the zeroes of the polynomial is .

Step 1: Use the identity:


Step 2: From the quadratic equation , we know:
- Sum of the roots
- Product of the roots

Step 3: Substitute in the identity:


Step 4: Take LCM:

The correct option is (C):