CLASSIFYING POLYNOMIALS EXPRESSIONS WORKSHEET

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

Write the degree of each polynomial.

Problem 1 :

3x⁴ + 2xyz + 5x² - 4

Solution

Problem 2 :

-6s²tu³ + st + tu² + st³u + t³

Solution

Problem 3 :

-d² - d – 9d³

Solution

Problem 4 :

uv + 4u

Solution

Problem 5 :

6u² + u²vw – 2u³vw + 4u³

Solution

Problem 6 :

3m⁵n²

Solution

Problem 7 :

p²q³r³ - p⁴qr² + 7 + qr + p⁶q

Solution

Problem 8 :

-8a² + abc + b²c² + ab

Solution

Problem 9 :

x – x⁶ + x² + x³ - x⁵

Solution

Problem 10 :

4r⁴ + r³s⁴t³ - r²s³t + t⁶ + 3

Solution

Problem 11 :

-q³rs² + 3 – q⁷r² + r²s⁴

Solution

Problem 12 :

w⁴xy⁵ – w⁶xy³ + 9w⁴x⁵y²

Solution

Problem 13 :

A polynomial of degree 7 is divided by a polynomial of degree 4. Find the degree of the quotient.

Solution

Problem 14 :

Write the degree of the given polynomials :

i) (2x + 4)³

ii) (t³ + 4) (t³ + 9)²

Solution

Problem 15 :

Write the coefficient of x⁴ and x in 4x³ -5x⁴ +2x² + 3.

Solution

Problem 16 :

Find the zeroes of f(z) = z² - 2z

Solution

Problem 17 :

Find the product using suitable identities: (4 + 5x)(4 - 5x).

Solution

Problem 18 :

What is the value of k in polynomial x² + 8x + k , if -1 is a zero of the polynomial?

Solution

Which of the following are polynomial functions? For those that are polynomial functions, state the degree and leading coefficient. For those that are not, explain why not.

Problem 1 :

f(x) = 4x³ - 5x – 1/2

Solution

Problem 2 :

g(x) = 6x^-4 + 7

Solution

Problem 3 :

h(x) = √(9x⁴ + 16x²)

Solution

Problem 4 :

k(x) = 15x – 2x⁴

Solution

Problem 5 :

f(x) = 3x^-5 + 17

Solution

Problem 6 :

f(x) = -9 + 2x

Solution

Problem 7 :

f(x) = 2x⁵ – 1/2x + 9

Solution

Problem 8  :

f(x) = 13

Solution

Problem 9 :

h(x) = (27x³ + 8x⁶)

Solution

Problem 10 :

k(x) = 4x – 5x²

Solution