Revision Notes: Class 10 Maths Chapter 2 Polynomials

A fast, one-glance recap of Class 10 Maths Chapter 2 (Polynomials) — for the full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 2 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

Common Mistakes Students Make in Polynomials

Why This Chapter Matters

Polynomials is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. It also builds the algebraic foundation for Chapter 4 (Quadratic Equations) and reappears in Class 11 algebra, so a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

Revision Notes: Polynomials

• Standard form (quadratic): p(x) = ax²+bx+c, where a, b, c are real numbers and a ≠ 0
• Zero (root) of a polynomial: a real number k such that p(k) = 0 — graphically, the x-coordinate(s) where the graph of y=p(x) crosses the x-axis
• Degree and zero count: a quadratic polynomial (degree 2) has at most 2 zeroes; a linear polynomial (degree 1) has exactly 1 zero
• Relationship between zeroes and coefficients (if α, β are the zeroes of ax²+bx+c): sum α+β = −b/a, product αβ = c/a
• Finding zeroes: factorise by splitting the middle term (find two numbers whose product is ac and sum is b), or apply the quadratic formula directly
• Constructing a polynomial from a given sum and product of zeroes: x² − (sum)x + (product) = 0, multiplying through by a suitable constant to clear fractions if needed
• Verification step: after finding zeroes, always check −(coefficient of x)/(coefficient of x²) equals your computed sum, and (constant term)/(coefficient of x²) equals your computed product
• 2023 rationalisation: the current syllabus keeps only Exercise 2.1 (finding zeroes of a quadratic and verifying the zero-coefficient relationship) — the earlier, pre-rationalisation edition also covered cubic polynomials, the division algorithm for polynomials, and the relationship between zeroes and coefficients of a cubic, all of which were removed
• Know by heart: sum = −b/a (note the minus sign) and product = c/a — the sign of the sum is the single most common slip in this chapter

See also: Extra Questions (HOTS) | Formulas Handbook

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Frequently Asked Questions

What is the relationship between the degree of a polynomial and its number of zeroes?
A polynomial of degree n can have at most n zeroes — so a linear polynomial has at most 1 zero, a quadratic at most 2, and a cubic at most 3.

What do the zeroes of a quadratic polynomial represent graphically?
They are the x-coordinates of the points where the graph of the polynomial (a parabola) intersects the x-axis — a quadratic can touch/cross the x-axis at 2 points, 1 point (a repeated zero), or 0 points depending on its discriminant.

What to Revise First (and Last) in This Chapter

Written by Satish

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