Q. 25.0( 1 Vote )

Factorize x4

Answer :

To factorize x4 + x2 + 1, consider the expression (x2 + 1)2.


We have the identity (a + b)2 = a2 + 2ab + b2


(x2 + 1)2 = x4 + 2x2 + 1


Rearranging terms in the equation by moving one x2 term to the left hand side, we have,


(x2 + 1)2 – x2 = x4 + x2 + 1


x4 + x2 + 1 = (x2 + 1)2 – x2


Using the identity (a + b)(a – b) = a2 – b2, we have,


x4 + x2 + 1 = [(x2 + 1) + x][(x2 + 1) – x]


x4 + x2 + 1 = (x2 + x + 1) (x2 – x + 1)


Hence, the factors of x4 + x2 + 1 are (x2 + x + 1) and (x2 – x + 1).


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Questions on FactorizationQuiz | Questions on FactorizationQuiz | Questions on Factorization41 mins
Quiz | Important Questions on FactorisationQuiz | Important Questions on FactorisationQuiz | Important Questions on Factorisation35 mins
NCERT | Factorisation ProblemsNCERT | Factorisation ProblemsNCERT | Factorisation Problems38 mins
Algebraic Identities - Mark your Weak AreasAlgebraic Identities - Mark your Weak AreasAlgebraic Identities - Mark your Weak Areas41 mins
Champ Quiz | Division of PolynomialsChamp Quiz | Division of PolynomialsChamp Quiz | Division of Polynomials33 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Factorize each ofRD Sharma - Mathematics