🎯 Polynomials Worksheet Practice
Polynomials Class 10 Worksheet – Complete Practice Guide
Polynomials is Chapter 2 of Class 10 Mathematics and is one of the most useful algebra topics for board-exam preparation. This online worksheet is built for repeated practice of the ideas students commonly meet in classroom exercises, revision sheets and examinations. It combines quick objective questions with numerical problems so learners can strengthen both concepts and calculation accuracy.
1. What Is a Polynomial?
A polynomial in one variable is an algebraic expression in which the powers of the variable are non-negative integers and the coefficients are real numbers. Examples include 3x + 2, x² − 5x + 6 and 7x³ + x − 4. The highest power of the variable with a non-zero coefficient determines the degree.
2. Zeroes of a Polynomial
A number k is called a zero of a polynomial p(x) if p(k) = 0. Graphically, the real zeroes of a polynomial are the x-coordinates where its graph meets or touches the x-axis. For a quadratic polynomial, there can be two, one or no real zeroes depending on the graph and coefficients.
3. Relationship Between Zeroes and Coefficients
If α and β are the zeroes of ax² + bx + c, then their sum and product can be found directly from the coefficients. These relationships are frequently useful because they avoid solving the entire equation when only the sum or product is required.
For a polynomial x² − (α + β)x + αβ, the zeroes are α and β. Practise moving between the zeroes and coefficients carefully. Pay particular attention to the negative sign in the sum formula.
4. Forming a Quadratic Polynomial
When the zeroes are known, their sum and product can be substituted into the standard form. For example, if the zeroes are 2 and 5, the polynomial can be written as x² − 7x + 10. Multiplying by any non-zero constant gives another polynomial with the same zeroes.
5. Division Algorithm and Remainder
Polynomial division expresses a dividend in terms of a divisor, quotient and remainder. The remainder theorem gives a quick way to evaluate the remainder when a polynomial is divided by x − a.
The factor theorem is closely connected: if p(a) = 0, then x − a is a factor of p(x). These results are valuable for checking factors and simplifying polynomial problems.
6. Graphs of Polynomials
The graph of a linear polynomial is a straight line, while a quadratic polynomial has a parabolic shape. The number of points where the graph crosses or touches the x-axis tells us about its real zeroes. A graph crossing the axis twice indicates two distinct real zeroes; touching once indicates a repeated real zero; and a graph that does not meet the axis has no real zeroes.
7. Using This Online Worksheet
Select the number of questions, question type, difficulty and optional timer. Press Start New Test. Every question has an answer box and its own Check Answer button. The correct answer stays hidden until checking. Correct entries turn green, incorrect entries turn red, and the progress bar records checked questions.
Shuffle Whole Worksheet creates a fresh randomized set with changing coefficients, zeroes, divisors and numerical values. Use Easy mode for learning, Medium for regular revision and Hard for challenge practice. You can turn sound off for silent study.
8. Exam Preparation Tips
Memorise the zero-coefficient relationships, but also understand where they come from. Substitute a suspected zero into p(x) to verify it. When forming a polynomial from zeroes, calculate the sum and product first. For division questions, distinguish clearly between divisor, quotient and remainder. Use the graph interpretation to connect algebraic zeroes with geometry.
9. Key Learning Checklist
This DigiSadhan worksheet is suitable for homework, classroom revision, self-study, quick tests and mobile learning. The Print Worksheet button opens the browser print dialog, while Save as PDF uses that same dialog with a PDF destination on supported devices.