UNDERSTANDING POLYNOMIALS WORKSHEET

State whether the statements given are true or false.

Problem 1 :

1 + x/2 + x³ is a  polynomial.

Solution

Problem 2 :

(3a - b + 3) - (a + b) is a binomial.

Solution

Problem 3 :

A trinomial can be a polynomial.

Solution

Problem 4 :

A polynomial with more than two terms is a trinomial.

Solution

Problem 5 :

Sum of x and y is x + y.

Solution

Problem 6 :

Sum of 2 and p is 2p.

Solution

Problem 7 :

A binomial has more than two terms.

Solution

Problem 8 :

A trinomial has exactly three terms.

Solution

Problem 9 :

In like terms, variables and their powers are the same.

Solution

Problem 10 :

The expression x + y + 5x is a trinomial.

Solution

Problem 11 :

4p is the numerical coefficient of q² in -4pq².

Solution

Problem 12 :

5a and 5b are unlike terms.

Solution

Problem 13 :

If we add a monomial and binomial, then answer can never be a monomial.                Solution

Problem 14 :

If we subtract a monomial from a binomial, then answer is atleast a binomial.           Solution

Problem 15 :

When we subtract a monomial from a trinomial, then answer can be a polynomial.         Solution

Problem 16 :

The amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x⁸ + 600x⁶, where x is the growth factor. Classify the polynomial by the number of terms. What is its degree?

Solution

Problem 17 :

The expression (4/3) πr³ represents the volume of a sphere with radius r. Why is this expression a monomial? What is its degree?

Solution

Problem 18 :

The number of individual memberships at a fitness center in m months is represented by 142 + 12m. The number of family memberships at the fitness center in m months is represented by 52 + 6m. Write a polynomial that represents the total number of memberships at the fitness center.

Solution

Give the name for the following polynomials based on power and degree of the polynomials.

Problem 1 :

3

Solution

Problem 2 :

-p² + 2

Solution

Problem 3 :

6x⁴ - 2x³

Solution

Problem 4 :

 5n⁴ - n² - 2

Solution

Problem 5 :

-2p⁴ + 10p⁶ + 5p²

Solution

Problem 6 :

9m + 5m² + 10m³ - 5

Solution

Problem 7 :

8n² - n³ + 7n

Solution

Problem 8 :

For the polynomial P(x) = 5x³ - 3x² + 2x + √2, mark the statements as true or false and justify.

a) The degree of the polynomial P(x) is 4.

b) The degree of the polynomial P(x) is 3.

c) The coefficient x² is 3

d) The coefficient x² is 2

e) The constant is 3

f) The number of terms is 4.

Solution

Problem 9 :

Justify the following statements with examples.

a) We can have a trinomial having degree 7.

b) The degree of a binomial cannot be more than two.

c) There is only one term of degree one in the monomial.

d) A cubic polynomial always has degree three

Solution

Problem 10 :

Complete the entries 

p(x) = 5x⁷ - 6x⁵ + 7x - 6

Coefficient of x⁵ = 

Degree of p(x) = 

Constant term = 

Number of terms = 

Solution

Problem 11 :

Which of the following is not a polynomial ?

a) x² + √2x + 3        b) x² - √2x + 6        c) x³ + 3x² - 3       d) 6x + 4

Solution

Problem 12 :

The degree of the polynomial 3x³ - x⁴ + 5x + 3 is 

a) 3    b)  -4     c) 4     d) 1

Solution

Problem 13 :

Which of the following is a term of the polynomial ?

a) 2x     b) 3/x   c) √x    d) √x ^√x

Solution

Problem 14 :

If p(x) = 5 x² - 3x + 7, then p(1) equals

a)  -10    b) 9     c) -9    d)  10

Solution