Question

Based on 5 situations, frame 5 questions on polynomials and answer the following questions-:a) Find the degree of polynomial and classify it as cubic or quadratic or linear. b) Classify it as a monomial or binomial or trinomial. c) Find the maximum number of zeroes it can have.

The 5 situations are:

1) The cube of a number added to 5 times the number and any constant subtracted from it.

2) Twice the number of candies in a person's bag added to square of the number of candies in hisher bag.

3) Four times the cube of any negative integer.

4) A number and its square added or subtracted.

5) Twice the cube of a number added to thrice the square of it and the number and a constant subtracted from it

Answer 1

Answer:

Let number = x

1 ) Our polynomial is As:

x ³ + 5x - C

Where C is a constant .
a) Here the highest degree of our number x is 3 , So this polynomial is cubic .
b) As we can see that our polynomial has three terms As ( x³ , ​ 5x And C ) So our polynomial is Trinomial .
c) The maximum number zeros depend on the highest power ( here that is 3 ) , so there are Three numbers of zeros it can have

2) Let number of candies = x
So our polynomial is As:

2 x + x²

a ) Here the highest degree of our number x is 2 , So this polynomial is Quadratic .
b) As we can see that our polynomial has two terms As ( x² , ​ 2x ) So our polynomial is Binomial .
c) The maximum number zeros depend on the highest power ( here that is 2 ) , so there are Two numbers of zeros it can have ​

3) Let our negative integer = -x

So our polynomial is As:
4( -x )³
- 4 x³

a) Here the highest degree of our number x is 3 , So this polynomial is cubic .
b) As we can see that our polynomial has one term As ( - 4 x³ ) So our polynomial is Monomial .
c) The maximum number zeros depend on the highest power ( here that is 3 ) , so there are Three numbers of zeros it can have

4) Let number = x

So our polynomial is As:

x + x² Or x - x²

a) Here the highest degree of our number x is 2 , So this polynomial is Quadratic .
b) As we can see that our both polynomial have two terms As ( x² , ​ x ) So our polynomial is Binomial .
c) The maximum number zeros depend on the highest power ( here that is 2 ) , so there are Two numbers of zeros it can have ​​

5) Let number = x , Constant = C
So our polynomial is As:

2x³ + 3x² + x - C

a) Here the highest degree of our number x is 3 , So this polynomial is cubic .
b) As we can see that our polynomial has four term As ( 2 x³ , 3x² , x , C ) So our polynomial is Quadnomial .
c) The maximum number zeros depend on the highest power ( here that is 3 ) , so there are Three numbers of zeros it can have ​