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CBSE Worksheet for chapter-4 Polynomial class 9

Worksheet For class 9

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Mathematic Worksheet - 4

TOPIC: Polynomial

For other CBSE Worksheet for class 9 Mathematic check out main page of Physics Wallah.



An algebraic expression f(x) of the form f(x)= a0 + a1x +a2x2+…….+an xn, where a0,a1, a2……. an are real numbers and all the index of x are non negative integers is called polynomial in x and the highest index n is called as the degree of polynomial.

Important Formulas

  • (x+a)2 =x2 +2ax+a2
  • (x-a)2 =x2 – 2ax +a2
  • x2-a2 =(x+a) (x-a)
  • x3+a3=(x+a) (x2-ax+a2)=(x+a)3 –3xa(x+a)
  • x3-a3=(x-a) (x2+ax+a2)=(x+a)3 +3xa(x-a)
  • (a + b + c) 2=a2+b2+c2+2ab+2bc+2ac
  • (a + b) 3= a3+b3+3ab (a + b)
  • (a-b) 3= a3-b3-3ab (a-b)
  • a3+b3+c3-3abc = (a +b +c) (a2+b2+c2-ab-bc-ca)
  • SPECIAL CASE : If a+ b +c=0 then a3+b3+c3=3abc

Zeros or Roots of a Polynomial

A real number ‘a’ is a zero of a polynomial f(x),if f(a)=0.Here ‘a’ is called a root of the equation f(x) = 0

Factor Theorem

Let p(x) be a polynomial of degree greater than or equal to ‘a’, be a real number such that p(a)=0,then (x-a) is a factor of p(x),then p(a) = 0.

Remainder Theorem

Let p(x) be any polynomial of degree greater than or equal to one and ‘a’ be any real number. If p(x)is a dividend by (x-a),then remainder is equal to p(a).let q(x) be the quotient and r(x) be the remainder when p(x) is divided by (x-a),then

Dividend=Divisor x Quotient + Remainder


Q1. Factors of (42-x-x2) are

  1. (x-7) (x-6)
  2. (x+7) (6-x)
  3. (x+7) (6-x)
  4. (x+7) (x+6)

Q2. Factors of are(x2+x/6-1/6)

  1. 1/6 (2x+1)(3x+1)
  2. 1/6 (2x+1)(3x-1)
  3. 1/6 (2x-1)(3x-1)
  4. 1/6 (2x-1)(3x+1)

Q3. Factors of polynomial are

  1. (x-2) (x+3) (x-4)
  2. (x-+) (x+3) (x+4)
  3. (x+2) (x-3) (x-4)
  4. (x-2) (x-3) (x-4)

Q4. If (x+a) is a factor of x2+pq+q and x2+mx+n then the value of a is

  1. (m-p)/(n-q)
  2. (n-p)/(m-q)
  3. (n+p)/(m+q)
  4. (m+p)/(n+q)


  1. Factorize x4+x3+7x2-x+6.
  2. Determine whether x-3 is a factor of polynomial p(x)= x3 3x2 +4x-12
  3. If p(x)= 4x4 +5x3 -12x2-11x+5,g(x)=4x+5
  4. Determine if (x+1) is a factor of (2-√2)x + √2
  5. Factorize the following polynomials:
    1. x3 -23x2+142x-120
    2. 2y3 +y2-2y-1
    3. x4 -5x2+4
    4. x3 -10x2-53x-42



  1. 3
  2. 2
  3. 1
  4. 2


  1. (x+1)(x-1)(x+3)(x-2)
  2. yes
  3. (x+1) is a factor
  4. (x-1)(x-10)(x-12)

For other CBSE Worksheet for class 9 Mathematics check out main page of Physics Wallah.

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