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Factorization of Cubic Polynomial

Polynomials II - Concepts

Algebraic Identity - Square of Sum of Binomial

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Dfference of Square

Algebraic Identity -3

Algebraic Identity - Square of Trinomial

Algebraic Identity - Difference of Cubes

Algebraic Identity - Sum of Cubes

Algebraic Identity -Cube of Sum of Binomial

Algebraic Identity -Cube of Difference of Binomial

Algebraic Identity- Conditional

Division of Polynomial by another Polynomial Long Division

Factorization of Cubic Polynomial

Relationship of Zeros With Coefficients of Cubic Polynomial

Factorisation Using Square Identities

Factorisation Using Cubic Identities

Class - 10th IMO Subjects

Concept Explanation

Factorization of Cubic Polynomial

Factorization of Cubic Polynomial: To factorise a cubic polynomial we perform the following steps:

Find a zero of the polynomial by hit and trial method

The perform long division of the polynomial by the factor obtained above

The quotient will be a polynomial of Degree 2

This quotient is then factorized by using the middle term spliting method.

Example: Factorise the following polynomial

$large x^3-6x^2+11x-6$

Solution: As it is a cubic polynomial one zero will be found using Factor Theorem

Puting the value of x= 1 in the polynomial we get

$large f(1)=(1)^3-6(1)^2+11(1)-6$

$large =1-6+11-6=0$

Therefore according to the Factor Theorem

x-1 is factor of the given polynomial

We will now perform long division with this factor

$large f(x)= x^3-6x^2+11x-6$

$large = (x-1)(x^2-5x-6)$

$large = (x-1)(x^2-6x+x-6)$

$large = (x-1)[x(x-6)+1(x-6)]$

$large = (x-1)(x-6)(x +1)$

Factorization of Bi-quadratic Polynomial: To factorise a bi-quadratic polynomial we perform the following steps:

Find two zeros of the polynomial by hit and trial method

Find the product of the two factors

The perform long division of the polynomial by the product of two factors obtained above

The quotient will be a polynomial of Degree 2

This quotient is then factorized by using the middle term spliting method.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

On dividing $large x^4+x^3+2x^2+3$ by a polynomial g(x), we get the quotient $large x^2+x+7$ and the remainder 5x + 38. The polynomial g(x) is
A. $large x^2+5$		B. $large x^2+7$
C. $large x^2-5$		D. $large x^2-7$
Right Option : C
View Explanation

Question : 2

If $large ax^3+bx^2+x-6$ has x + 2 as a factor and leaves a remainder 4 when divided by ( x - 2 ), find the values of a and b.
A. 0,-2	B. 2,3	C. -2,3	D. 0 , 2
Right Option : D
View Explanation

Question : 3

The number of zeroes in the polynomial $large x^3-2x^2+x-2$ is ______________-
A. 4	B. 1	C. 2	D. 3
Right Option : D
View Explanation

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Language - English

Chapters

Real Numbers I

Real Numbers II

Pair of Linear Equations I

Pair of Linear Equations II

Polynomial I

Polynomials II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Triangles I

Triangles II

Some Applications of Trigonometry

Coordinate Geometry I

Coordinate Geometry II

Introduction to Trigonometry

Direct and Inverse Variation

Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

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Factorization of Cubic Polynomial

Factorization of Cubic Polynomial

Students / Parents Reviews [10]

Shivam Rana

Yatharthi Sharma

Cheshta

Barkha Arora

Shreya Shrivastava

Om Umang

Ayan Ghosh

Hiya Gupta

Manish Kumar

Aman Kumar Shrivastava