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

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Solution

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

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Similar questions

Q. What constant number must be added or subtracted to

4 x^{2} + 12 x + 8 = 0

to solve it by method of completing the square?

Q. In the following questions the following rules have been applied to the same set of numbers In every question find out which of the rules viz (1), (2), (3), (4) and (5) have been applied
Rules:
(1) Subtract thrice the number from its cube
(2) Multiply the number by 7 and subtract 3 from the result
(3) Add the number to its square
(4) Divide the number by 2 and add the square of the quotient to the number
(5) Multiply the number by 5 and add 5 to the result
20, 42, 72, 110

Four times a number added to thrice another number gives 43. Twice the second number, subtracted from thrice the first gives 11. What are the numbers?

Question 33

Fill in the blanks to make the statement true.

If 5 is added to three times a number, it becomes the same as 7 is subtracted from four times the same number. This fact can be represented as ..............

Get the algebraicexpressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y.

(ii) One-half of the sum of numbers x and y.

(iii) The number z multiplied by itself.

(iv) One-fourth of the product of numbers p and q.

(v) Numbers x and y both squared and added.

(vi) Number 5 added to three times the product of number m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii)Sum of numbers a and b subtracted from their product.

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