CBSE Worksheet for chapter4 Polynomial class 9
Worksheet For class 9
Find CBSE Worksheet for chapter3 Polynomial class 9
CLASS9
BOARD: CBSE
Mathematic Worksheet  4
TOPIC: Polynomial
For other CBSE Worksheet for class 9 Mathematic check out main page of Physics Wallah.
Summary
An algebraic expression f(x) of the form f(x)= a_{0} + a_{1}x +a_{2}x^{2}+…….+a_{n }x^{n}, where a_{0},a_{1,} a_{2}……. a_{n }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} =x^{2 }+2ax+a^{2}
 (xa)^{2} =x^{2} – 2ax +a^{2}
 x^{2}a^{2} =(x+a) (xa)
 x^{3}+a^{3}=(x+a) (x^{2}ax+a^{2})=(x+a)^{3} –3xa(x+a)
 x^{3}a^{3}=(xa) (x^{2}+ax+a^{2})=(x+a)^{3} +3xa(xa)
 (a + b + c)^{ 2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ac
 (a + b) ^{3}= a^{3}+b^{3}+3ab (a + b)
 (ab) ^{3}= a^{3}b^{3}3ab (ab)
 a^{3}+b^{3}+c^{3}3abc = (a +b +c) (a^{2}+b^{2}+c^{2}abbcca)
 SPECIAL CASE : If a+ b +c=0 then a^{3}+b^{3}+c^{3}=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 (xa) 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 (xa),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 (xa),then
Dividend=Divisor x Quotient + Remainder
Objective
Q1. Factors of (42xx^{2}) are
 (x7) (x6)
 (x+7) (6x)
 (x+7) (6x)
 (x+7) (x+6)
Q2. Factors of are(x^{2}+x/61/6)
 1/6 (2x+1)(3x+1)
 1/6 (2x+1)(3x1)
 1/6 (2x1)(3x1)
 1/6 (2x1)(3x+1)
Q3. Factors of polynomial are
 (x2) (x+3) (x4)
 (x+) (x+3) (x+4)
 (x+2) (x3) (x4)
 (x2) (x3) (x4)
Q4. If (x+a) is a factor of x^{2}+pq+q and x^{2}+mx+n then the value of a is
 (mp)/(nq)
 (np)/(mq)
 (n+p)/(m+q)
 (m+p)/(n+q)
Subjective
 Factorize x^{4}+x^{3}+7x^{2}x+6.
 Determine whether x3 is a factor of polynomial p(x)= x^{3} 3x^{2} +4x12
 If p(x)= 4x^{4} +5x^{3} 12x^{2}11x+5,g(x)=4x+5
 Determine if (x+1) is a factor of (2√2)x + √2

Factorize the following polynomials:
 x^{3} 23x^{2}+142x120
 2y^{3} +y^{2}2y1
 x^{4} 5x^{2}+4
 x^{3} 10x^{2}53x42
Solutions
Objective
 3
 2
 1
 2
Subjective
 (x+1)(x1)(x+3)(x2)
 yes
 (x+1) is a factor
 (x1)(x10)(x12)
For other CBSE Worksheet for class 9 Mathematics check out main page of Physics Wallah.
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