Polynomials Notes

✓ Free notes Class 10 Math 1 study file

About these notes

Class 10 Math Polynomials notes for CBSE students give concise definitions, key formulas and worked steps to find zeroes, factorise quadratics and apply the factor and remainder theorems. Main sub-topics: degree and leading coefficient, division algorithm and synthetic division, factor theorem, remainder theorem, relation between zeros and coefficients (for ax²+bx+c), forming x² − Sx + P, multiplicity of roots and examples (like x² − 15 with roots ±√15). Ideal for Class 10 revision, school tests and CBSE board practice; use these notes with Merit Spring ROH chapter tests and mock tests to practise important questions, MCQ and question answer revision.

Key points you will learn

Class 10 Math Polynomials notes: definition, degree, leading coefficient and standard form
Zeroes (roots) and factor theorem: if P(α)=0 then (x−α) is a factor (गुणनखंड)
Remainder theorem and synthetic division to get remainder P(k) when dividing by (x−k)
Relation between zeros and coefficients: for ax²+bx+c, sum = −b/a and product = c/a
Form monic quadratic from sum S and product P as x² − Sx + P; check discriminant Δ = S² − 4P
Factorisation: write quadratic as (x − α)(x − β) once zeros α, β known; handle repeated roots
Check a candidate root by substitution or synthetic division; irrational roots like ±√15 valid

What is inside this chapter

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Polynomials

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Questions students ask

What is a polynomial?

A polynomial is an expression of the form a_n x^n + a_{n−1} x^{n−1} + … + a_0 where coefficients a_i are constants and n is a non-negative integer. Degree is the highest power with non-zero coefficient and determines shape and roots.

How to verify the relationship between zeroes and coefficients?

Find the roots α and β, then directly compute α+β and αβ; for ax²+bx+c check α+β = −b/a and αβ = c/a. You can also expand (x−α)(x−β) to compare coefficients.

How to form a quadratic when sum and product are given?

For given sum S and product P, write the monic quadratic x² − Sx + P as the required polynomial. Multiply by a constant a if a non-monic quadratic is needed and check discriminant for real roots.

How to check if k is a zero of a polynomial?

Substitute k into P(x): if P(k)=0 then k is a zero and (x−k) is a factor. Alternatively use synthetic division: zero remainder confirms (x−k) divides the polynomial.

Where to find Class 10 Math Polynomials notes and practice tests?

Merit Spring ROH hosts Polynomials notes; use the site’s chapter tests and mock tests for practice and check the platform for important questions and MCQ practice to strengthen revision and exam preparation.

More Math chapters

Real Numbers Pair of Linear Equations in Two Variables Quadratic Equations Arithmetic Progressions Triangles Coordinate Geometry All chapters →

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