case study question | polynomials 🔥| extra hots questions| part 3 | class 9

Описание: polynomials 🔥🔥| extra hots questions 🤯| part 3 | class 9 | ncert #maths #infinixclasses #youtube


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Question - 12: Factorise x^6 - y^б.


CASE STUDY/SOURCE BASED QUESTIONS
In Class IX, mathematics teacher asked to students about polynomials, which has variables x and y. Then out of these polynomials, following are represented by p(x) = 4x2 − 2x + 2 at x = 2, q(y) = y2 − 2y + 1 at y = 1 and r(t) = t2 + 6t + 8 at t = 2. Then students solved these equations to get best appreciation from teacher side and to exchange themselves practice for doing excellent performance in half yearly and yearly exams.
Based on the above information, answer the following questions.
(i) Calculate the value of polynomial p(x) = 4x2 − 2x + 2 at x = 2.
(ii) Calculate the zeros of the given g(y) = y2 − 2y + 1
(iii) Find the value of zeros of r(t) = t2 + 6t + 8
Or
How many zeros are there in a linear polynomial?


Case Study 2: Gardening Project
Context:A group of Class 9 students decided to plant flowers in a rectangular garden. They observed that the area of the garden is expressed as the polynomial:A(x) = 4x2 + 12xwhere x is the length in meters, and the breadth is expressed as a linear polynomial.
Questions:
Identify the type of polynomial A(x) = 4x2 + 12x.
Find the highest degree term of the polynomial.
Factorize A(x).
If the length of the garden is x, find the breadth of the garden in terms of x.
If x = 3, find the numerical area of the garden.


Case Study 3: Toy Car Factory
Context:A toy manufacturing company calculates the cost (in ₹) of making a toy car using the polynomial:C(x) = x3 − 3x2 + 4x − 12where x is the number of parts used in each toy.
Questions:
What is the degree of the polynomial C(x)?
Find the value of C(2).
Verify whether x = 3 is a zero of C(x).
Find the remainder when C(x) is divided by x − 1.
What is the constant term in the polynomial?


Case Study 4: Road Construction Project
Context:An engineer uses the polynomial expression for the total cost (in ₹):T(x) = x2 + 5x + 6where x is the number of kilometers of road built.
Questions:
Factorize the polynomial T(x).
Find the value of T(2).
What are the zeroes of the polynomial?
Is x = −2 a zero of the polynomial? Justify.
Identify the coefficient of x2.


Case Study 5: Sales Profit Model
Context:A company models its profit in a week using the polynomial:P(x) = x3 + 2x2 − 5x − 6where x is the number of units sold in hundreds.
Questions:
Find the value of P(−1).
Use factor theorem to check if x = −1 is a zero of P(x).
Find any one factor of the polynomial.
What is the degree and leading coefficient of P(x)?
Write down the constant term.