Chapter 2 · NCERT Class 9 Mathematics

Polynomials

An algebraic expression built from terms with whole-number powers — like 2x² + 3x − 5. Learn to read its degree, coefficients and constant term, name it by degree, and find the values that make it zero. Tap each term to see exactly what it means.

📐 3 topics⏱ ~25 min📝 12-question quiz

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The language of polynomials

A polynomial has its own vocabulary. Tap each term to see what it points to in 2x² + 3x − 5 and how the pieces fit together.

Explore · Reading 2x² + 3x − 5tap a term

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The three big ideas

Polynomial — an expression made of terms in a variable, where every power of the variable is a whole number, e.g. 2x² + 3x − 5.
Degree — the highest power of the variable. In 2x² + 3x − 5 the degree is 2.
Coefficient — the number multiplying a power of the variable. In 2x² the coefficient is 2; the coefficient of x is 3.
Constant term — the term with no variable. Here it is −5.

Common mistake: in a polynomial the powers must be whole numbers (0, 1, 2, 3, …). Terms like √x (which is x^½) or 1/x (which is x⁻¹) are not polynomial terms — so √x + 3 and 1/x + 2 are not polynomials.

Linear — degree 1, like 2x + 5. Its graph is a straight line.
Quadratic — degree 2, like x² − 4x + 3.
Cubic — degree 3, like x³ − 2x + 1.
A non-zero constant such as 7 has degree 0; the degree of the polynomial names its type.

A zero (or root) of p(x) is a value of x for which p(x) = 0.
To find the zero of a linear polynomial ax + b, set it equal to 0 and solve: x = −b/a.
On a graph, a zero is where the curve crosses the x-axis.

Worked example. Give the degree of 5x³ − 2x + 7, and find the zero of 2x − 6.

Degree: the highest power is x³, so the degree is 3 — a cubic polynomial.

Zero of 2x − 6: set 2x − 6 = 0 ⇒ 2x = 6 ⇒ x = 3.

Where you'll meet it

Polynomials, at work

Areas & projectile paths

The area of a rectangle of sides x and x + 5 is the quadratic x² + 5x; the height of a thrown ball over time follows a quadratic like −5t² + 20t. Degree-2 polynomials describe these everyday shapes.

Graphs & formulas

Straight lines (linear), curves (quadratic, cubic) and many physics and finance formulas are polynomials. Reading degree, coefficients and zeroes lets you predict and plot how a quantity behaves.