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Chapter 3: Polynomials

    Introduction

    What are Polynomials?

    Working With Polynomials

    Geometrical Meaning of the Zeroes of a Polynomial

    Relationship between Zeroes and Coefficients of a Polynomial

    Cubic Polynomials

    Division Alogorithm For Polynomials

    What We Have Discussed

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 3: Polynomials > Enhanced Curriculum Support

Enhanced Curriculum Support

This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:

Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.

Exam Preparedness: Sample Question Papers provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.

Sample Questions

About the Section

Sec A

(1) If x4 + 3x2 + 7 is divided by x + 3, then the possible degrees of quotient and remainder are .....
(A) 3, 0 (B) 4, 1 (C) 3, 1 (D) 4, 0

(2) If p(x) = 5x4 + 6x2 + 3x - 7, then p(0) is ......
(A) 5 (B) 3 (C) 6 (D) -7

(3) Choose the correct answer satisfying the following statements.

Statement (A) : Number of maximum zeroes of a cubic polynomial is 3.

Statement (B) : Zero of a linear polynomial x-2 is -2

(i) Both (A) and (B) are TRUE. (ii) (A) is TRUE, (B) is FALSE (iii) (A) is FALSE, (B) is TRUE. (iv) Both (A) and (B) are FALSE.

(4) If P(x) = x4 + 1, then find P(2) - P(-2).

(5) If the zeroes of the polynomial x2 + (a + 1)x + b are 2 and -3, then the values of a and b are .....
(A) a = -5, b = -1 (B) a = 5, b = -1 (C) a = -2, b = 6 (D) a = 0, b = -6

(6) The first degree equation in two variables ax + by + c = 0 represents ......
(A) Straight line (B) Parabola (C) Line segment (D) Ray

(7) If P(x) = x4 + 1, then find P(2) - P(-2).

(8) Verify the relation between zeroes and coefficients of the Quadratic polynomial x2−4.

Sec B

(1) If p(x) = x2+3x+4, then find the values of p(0) and p(1).

(2) Divide x3−4x2+5x−2 by x−2.

(3) Divide x3−4x2+5x−2 by x−2.

(4) Complete the following table for the polynomial: y = p(x) = x3−2x+3.

x-1012
x3
-2x
3
y
(x, y)

Sec C

(1) Total number of pencils required are given by 4x4+2x3−2x2+62x−66. If each box contains x2 + 2x - 3 pencils, then find the number of boxes to be purchased.

(2) Find the zeroes of the polynomial x² + 7x + 10 and verify the relation between the co-efficients of the polynomial and the zeroes of the polynomial.

(3) Draw the graph of the polynomial p(x) = x2−7x+12, then find its zeroes from the graph.

OR

Solve the equations graphically 3x+4y=10 and 4x−3y=5.

(4) Draw the graph of the polynomial p(x) = x2−7x+12, then find its zeroes from the graph.

Sec D

(1) Draw the graph of the Quadratic polynomial p(x) = x2+x−12 and find the zeroes of the polynomial from the graph.

(2) Draw the graph of the quadratic polynomial p(x) = x2−4x+3 and find the zeroes of the polynomial from the graph.

(3) Draw the graph of the polynomial p(x) = x2 + 2x – 3 and find zeroes of the polynomial from the graph.

Sec E

(1) Draw the graph of the polynomial P(x) = x² - 2x - 8 and find its zeroes.

(2) Draw the graph of the polynomial p(x) = x2+2x−3 and find the zeroes of the polynomial from the graph.