Virtual Labs

1. Which pair of values correctly represents the term

-4x^5

in a polynomial linked-list node?

(5,-4)

Explanation

(-4,5)

Explanation

(4,-5)

Explanation

(-5,4)

Explanation

2. When representing the polynomial

6x^3 - 2x + 9

as a linked list, how many term nodes are required?

a: 2 Explanation

Explanation

b: 3 Explanation

Explanation

c: 4 Explanation

Explanation

d: 9 Explanation

Explanation

3. During polynomial addition, what should happen when the current exponents are equal?

a: Add the coefficients and create one result term with that exponent Explanation

Explanation

b: Add the exponents and keep both coefficients Explanation

Explanation

c: Discard both terms Explanation

Explanation

d: Multiply the coefficients and exponents Explanation

Explanation

4. What is the result of adding

3x^2 + 4x

and

5x^2 - x

8x^4 + 3x

Explanation

2x^2 + 5x

Explanation

8x^2 + 3x

Explanation

15x^2 - 4x

Explanation

5. What is the result of subtracting

2x^2 + 3x

from

7x^2 + x

9x^2 + 4x

Explanation

5x^2 - 2x

Explanation

14x^2 + 3x

Explanation

5x^2 + 4x

Explanation

6. Two polynomial linked lists contain

m

and

n

nodes. What is the time complexity of multiplying the two polynomials using the straightforward term-by-term approach?

O(1)

Explanation

O(m+n)

Explanation

O(\log(m+n))

Explanation

O(mn)

Explanation

7. Why is it necessary to combine terms with the same exponent after polynomial multiplication?

a: To change every exponent to zero Explanation

Explanation

b: To ensure the result is simplified and equivalent terms are represented together Explanation

Explanation

c: To remove all coefficients from the result Explanation

Explanation

d: To make every linked list contain the same number of nodes Explanation

Explanation

8. If

2x^3

is multiplied by

5x^2

, what term is produced before combining it with any other like terms?

10x^5

Explanation

7x^6

Explanation

10x^6

Explanation

7x^5

Explanation

9. Which statement best describes polynomial addition using two linked lists ordered by decreasing exponent?

a: Every node in the first list must be compared with every node in the second list Explanation

Explanation

b: Only the first node of each list is used Explanation

Explanation

c: The lists can be processed sequentially by comparing current exponents Explanation

Explanation

d: The lists must first be converted into arrays Explanation

Explanation

Polynomial Arithmetic