Polynomials

Question 1

What is a variable?

Answer 1

variable is denoted by a symbol that can take any real value. We use the letters x, y, z, etc. to denote variables

Question 2

What is an Algebraic expressions?

Answer 2

An expression consisting of arithmetic numbers, letters (used as symbols) and operation signs is called an Algebraic Expression

Question 3

What is a polynomials in one variable mean?

Answer 3

Own answer

Question 4

What are the terms in expression x^2+2x ?

Answer 4

x^2 and 2x

Question 5

A polynomial can have ____ number of terms

Answer 5

Infinite

Question 6

What is a monomial?

Answer 6

Polynomials having only one term

Question 7

What is a binomial?

Answer 7

Polynomials having only two terms

Question 8

What is a trinomial?

Answer 8

Polynomials having only three terms

Question 9

True Or False Is the expression a Polynomial and why ?t(y) = y4 + y + 5

Answer 9

True

Question 10

p(x) = 3x⁷ – 4x + x + 9

What is the term with the highest power of x ?

Answer 10

It is 3x⁷

Question 11

p(x) = 3x⁷ – 4x + x + 9

The exponent of x in this term is _____

Answer 11

7

Question 12

In the polynomial q(y) = 5y⁶ – 4y² – 6

1. What is the term with the highest power of y?
2. What is the exponent ?
3. The degree of the polynomial

Answer 12

5y⁶ & 6 & 7

Question 13

What is the highest power of the variable in a polynomial called?

Answer 13

Degree of the polynomial

Question 14

The degree of a non-zero constant polynomial is ____

.

Answer 14

Zero

Question 15

Find the degree of each of the polynomials given below:

(i) x⁵ – x⁴ + 3
(ii) 2 – y² – y³ + 2y⁸
(iii) 2

Answer 15

(i) The highest power of the variable is 5. So, the degree of the polynomial is 5.
(ii) The highest power of the variable is 8. So, the degree of the polynomial is 8.
(iii) The only term here is 2 which can be written as 2 x⁰. So the exponent of x is 0. Therefore, the degree of the polynomial is 0.

Question 16

Find the coefficient of x3, x2 and x in

-x³ + 4x² + 7x – 2,

Answer 16

The coefficient of x³ is –1

The coefficient of x² is 4

The coefficient of x is 7

The coefficient of –2 is x⁰

(Remember, x0 = 1)

Question 17

What is a zero polynomial?

Answer 17

The constant polynomial 0 is called the zero polynomial

Question 18

True or False

I/x = x^-1

Is the abvoe expression a polynomial ?

Answer 18

True , No

Question 19

Cube root of y + y²? It is also not a polynomial (Why?)

Answer 19

Since the exponent 1/3 is not a whole number , this expression is not a polynomial

Question 20

What is a linear polynomial?

Answer 20

A polynomial of degree one is called a linear polynomial.

Question 21

Find a find a polynomial in x with 3 terms?

Answer 21

Not possible, linear polynomial in x can have at most two terms

Question 22

What is a quadratic polynomial?

Answer 22

A polynomial of degree two is called quadratic polynomial

Question 23

What is a cubic polynomial?

Answer 23

A polynomial with degree three is called a cubic polynomial