## Answer :

=[ a(x+1)^2+b(x+1)+c ] - [ax^2+bx+c]

=[ a(x^2+2x+1) +bx + b + c ] - [ax^2 + bx + c]

=[ ax^2 + 2ax + a + bx + b + c ] - [ax^2 + bx + c]

= ax^2 + 2ax + a + bx + b + c - ax^2 - bx - c

= 2ax + a + b

Therefore g(x) = 2ax + a + b

h(x) = g(x+1) - g(x)

=2a (x+1) + a + b - [2ax+a+b]

=2ax + 1 + a +b - 2ax - a - b

Therefore h(x) = 1