Polynomial Arithmetic

1. Which two pieces of information are essential for representing a polynomial term in a linked-list node?

a: Coefficient and exponent Explanation

Explanation

b: Node index and memory address Explanation

Explanation

c: Exponent and next node only Explanation

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d: Coefficient and list length Explanation

Explanation

2. How should the constant term

-6

be represented as a coefficient-exponent pair?

(0,-6)

Explanation

(-6,1)

Explanation

(-6,0)

Explanation

(6,0)

Explanation

3. In a linked-list representation of a polynomial, what does the pointer field of a node primarily provide?

a: The exponent of the next term Explanation

Explanation

b: A link to the next node Explanation

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c: The coefficient of the current term Explanation

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d: The degree of the polynomial Explanation

Explanation

4. When adding two polynomial linked lists, what is the correct action when the current exponents are equal?

a: Add the exponents Explanation

Explanation

b: Subtract the coefficients Explanation

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c: Ignore both nodes Explanation

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d: Add the coefficients and keep the common exponent Explanation

Explanation

5. When adding two polynomial linked lists, the current exponent in the first list is

5

and in the second list is

3

. Which term should be processed before the other?

a: The term with exponent

5

Explanation

b: The term with exponent

3

Explanation

c: Both terms must be multiplied Explanation

Explanation

d: Neither term should be processed Explanation

Explanation

6. What should happen to a term from one polynomial when its exponent does not occur in the other polynomial during addition?

a: Its coefficient should be multiplied by zero and the term discarded Explanation

Explanation

b: Its exponent should be changed to match the other term Explanation

Explanation

c: The term should be copied to the result without combining it with a term from the other polynomial Explanation

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d: The entire polynomial should be discarded Explanation

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7. In straightforward multiplication of two polynomial linked lists, why can the result initially contain multiple terms with the same exponent?

a: Because the pointer field changes the exponent Explanation

Explanation

b: Because different pairs of input terms can produce the same sum of exponents Explanation

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c: Because coefficients are stored as pointers Explanation

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d: Because linked lists cannot store unique exponents Explanation

Explanation

8. What is the result of multiplying

(2x^3)(-4x^2)

-8x^6

Explanation

-6x^5

Explanation

8x^5

Explanation

-8x^5

Explanation

9. Which statement best explains why linked lists are useful for sparse polynomial representation?

a: They require every possible exponent to be stored Explanation

Explanation

b: They can store only the terms that are present, avoiding nodes for missing terms Explanation

Explanation

c: They provide direct indexing by exponent Explanation

Explanation

d: They eliminate the need for polynomial arithmetic Explanation

Explanation