CBSE Class 10 Maths Polynomials: Chapter Guide

Polynomials usually follows Real Numbers on the CBSE Class 10 Maths syllabus, and for a lot of schools it falls inside the portion covered by the half-yearly or first-term exam. It's a short chapter built on a handful of ideas tested in slightly different forms, which is exactly why small, repeatable mistakes cost more marks here than the difficulty of the maths would suggest.

What the Chapter Actually Covers

The current syllabus keeps Polynomials focused on reading and relating, not long division. Two ideas carry almost the entire chapter:

• Zeroes of a polynomial and their graphical meaning. A zero is a value of x where the polynomial equals zero, and on a graph that shows up as the point where the curve crosses or touches the x-axis. A linear polynomial's graph is a straight line with at most one zero; a quadratic's is a parabola with at most two; a cubic's graph can have at most three. Reading a graph and stating how many zeroes it has, and whether they're real, distinct, or repeated, is one of the most frequently asked question types in this chapter.
• The relationship between zeroes and coefficients of a quadratic polynomial. For a quadratic ax² + bx + c, the sum of its zeroes always equals -b/a and the product always equals c/a. This works in both directions: given the polynomial, find the sum and product of its zeroes without solving for them individually; or given the sum and product (or the zeroes themselves), write the quadratic polynomial that produces them.

Polynomials sits inside CBSE's Algebra unit, which carries 20 of the 80 marks in the board paper across four chapters - Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, and Arithmetic Progressions - so this chapter on its own is a smaller, faster win rather than a heavily-weighted one.

What's No Longer in the Syllabus

The older version of this chapter included an exercise on the division algorithm for polynomials - a method for dividing one polynomial by another to get a quotient and remainder, often used to find a polynomial's remaining zeroes once one zero was already known. CBSE's rationalisation removed that exercise, and the questions built on it, entirely from what's currently assessed. As with Real Numbers, a lot of guidebooks, solved-example PDFs, and video walkthroughs still in circulation were written before this change and continue to work through long division of polynomials in detail. There's nothing wrong with that maths, but time spent on it this week is time not spent on graph-reading and the zero-coefficient relationship, which is what current papers actually ask.

Where Students Actually Lose Marks

• Dropping the negative sign in the sum of zeroes. The sum of zeroes is -b/a, not b/a. When b is already negative, the two negatives cancel out, and it's exactly this kind of sign-on-sign moment where a careless answer goes wrong.
• Miscounting zeroes from a graph. A curve that touches the x-axis at exactly one point without crossing it has two equal, repeated zeroes - not one - and a parabola that never touches the x-axis at all has no real zeroes, not "an answer waiting to be found." Both cases trip up students who expect every quadratic's graph to behave the same way.
• Mixing up the two directions of the same idea. Finding the sum and product from a given polynomial, and building a polynomial from a given sum and product, use the same formula read in opposite directions. Students who have only practised one direction often freeze, or misapply the formula, when a question asks for the other.

A Practical Way to Study This Chapter

• Practice reading eight to ten graphs cold. For each one, state the degree of the polynomial, how many times the graph meets the x-axis, and whether the zeroes are real, repeated, or absent - out loud or in writing, without a textbook open next to you.
• Drill both directions of the coefficient relationship. Take five quadratics and find the sum and product of their zeroes; then take five sum-and-product pairs and write the quadratic each one produces. Practising only one direction leaves half the chapter untested until the exam does it for you.
• Leave old division-algorithm questions alone. If a guidebook, an older sibling's notes, or a video walks through dividing one polynomial by another, that time is better spent redoing graph-reading and coefficient problems - what's currently being examined.
• Take a short, chapter-only test before starting Pair of Linear Equations. Confirming this chapter is solid now is quicker than discovering a gap during full-syllabus revision later in the term.

Where IndiaSchool.ai Fits

IndiaSchool.ai has a free AI lesson and unlimited board-pattern practice for every chapter of CBSE Class 10 Maths, including Polynomials, built around the current rationalised syllabus so practice time never goes toward an exercise that's already been dropped. A chapter-only paper, limited to what's currently examined, takes under two minutes to generate from the custom question paper tool, and the full Class 10 Maths chapter list is always visible on the syllabus explorer. One subscription, at ₹500 a month or ₹5,000 a year, covers every board and subject on the platform, with a 14-day free trial that needs no card to start.

The Bottom Line

Polynomials rewards the same kind of precision Real Numbers did: knowing the division algorithm is gone saves study time, and getting the sign in -b/a right, reading a graph's zeroes correctly, and working the coefficient relationship in both directions banks the rest. Get this chapter solid, and Pair of Linear Equations - the next stop on the syllabus - starts from a genuine foundation instead of a shaky one.