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CBSE Class 9 Mathematics Question 1 of 16

Polynomials — Question 2

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Question 2

Write the coefficients of x2 in each of the following:

(i) 2 + x2 + x

(ii) 2 - x2 + x3

(iii) π2\dfrac{π}{2} x2 + x

(iv) 2\sqrt{2}x - 1

Answer

(i) 2 + x2 + x

Coefficient of x2 is 1.

(ii) 2 - x2 + x3

Coefficient of x2 is (-1).

(iii) π2\dfrac{π}{2} x2 + x

Coefficient of x2 is = π2\dfrac{π}{2}

(iv) 2\sqrt{2}x - 1

Coefficient of x2 is 0.

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Mathematics | PolynomialsWeb Content • Interactive Notes

Polynomials — Interactive Study Guide

Master polynomial basics, Remainder and Factor Theorems, factorisation, and algebraic identities.

Polynomial Classification

Not a polynomial: √x (fractional power), 1/x = x−1 (negative power), x + 1/x.

Polynomial: 5 (constant), 3x + 2 (linear), x² − 1 (quadratic), 2x³ + x − 1 (cubic).

Remainder and Factor Theorems — Quick Guide

Remainder Theorem: When p(x) is divided by (x − a), remainder = p(a).
Factor Theorem: (x − a) is a factor of p(x) ⇔ p(a) = 0.

Watch the sign! Dividing by (x + 3) means a = −3. So remainder = p(−3).

Identity Mastery Checklist

See This PatternUse This Identity
a² + 2ab + b²= (a + b)²
a² − 2ab + b²= (a − b)²
a² − b²= (a + b)(a − b)
a³ + b³= (a + b)(a² − ab + b²)
a³ − b³= (a − b)(a² + ab + b²)
a + b + c = 0⇒ a³ + b³ + c³ = 3abc

Quick Self-Check

  1. Degree of 5x³ − 2x + 1? (3)
  2. Remainder when x² + 3x + 2 is divided by (x + 1)? (p(−1) = 1 − 3 + 2 = 0)
  3. Expand: (2a + 3b)² (= 4a² + 12ab + 9b²)
  4. Factorise: 8x³ − 27 (= (2x − 3)(4x² + 6x + 9))

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