Q. 3 A5.0( 1 Vote )

# By adding a number to p(x) = x3 + x2 + x, a new polynomial q(x) is to be formed.What number should be added, so that x – 1 is a factor of q(x)?

Given p(x) = x3 + x2 + x

Let the number to be added be “k”.

Then, the new polynomial q(x) = x3 + x2 + x + k

Now, (x – 1) is a factor of x3 + x2 + x + k.

i.e. x = 1 is the root of the polynomial.

Then, put the polynomial to zero we get,

x3 + x2 + x + k = 0

(1)3 + (1)2 + 1 + k = 0

1 + 1+1 + k = 0

k = – 3

Hence, “ – 3” should be added to the polynomial such that (x – 1) is a factor of q(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 |Revealing the relation Between Zero and Coefficients38 mins  Relation Between zeroes and Coefficients46 mins  Interactive Quiz - Geometrical Meaning of the Zeroes32 mins  Relationship between Zeroes and Coefficients-238 mins  Quiz - Division Algorithm38 mins  Relationship between Zeroes and Coefficients-152 mins  Interactive Quiz:Polynomials43 mins  Division Algorithm-130 mins  Relation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins  Solving Imp. Qs. of Olympiad on Polynomials47 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 