Question

What number should be added to the polynomial p(x) = x² + x – 1, so that (x – 2)is a factor of the new polynomial.

Answer 1

p (x) = x² + x – 1, remainder p(2) (1) 

p (2) = (2)² + 2 – 1 = 5 (1) 

For x – 2 to become a factor of p (2) must be equal to zero. 

For p (2) = 0 here we have to substract 5 from p(x). (1) 

That is, add –5 to p(x) for (x – 2) become a factor. (1)