Q. 2 B5.0( 6 Votes )

Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:

f(x) = x3 + 3x2 + 3x + 1, g(x) = x + 1

Answer :

By Factor Theorem, we know that,

If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0

For checking (x+1) to be a factor, we will find f(–1)

f(–1) = (–1)3 + 3(–1)2 + 3(–1) + 1

f(–1) = – 1 + 3 – 3 + 1

f(–1) = 0

As, f(–1) is equal to zero, therefore, g(x) = (x+1) is a factor f(x)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Polynomials29 mins
Polynomials - Zero to Hero42 mins
Genius Quiz | Polynomials40 mins
Genius Quiz | Division of Algebraic Expressions37 mins
Methods to find zeroes of a Polynomial-246 mins
Remainder Theorem and Factor Theorem38 mins
Introduction to Polynomials37 mins
Quiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of Polynomials37 mins
QUiz on Previous year NTSE Questions45 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
view all courses