Problema Solution
consider the polynomial p(x)=x^3-4x^2+ax-3. find a if, when p(x) is divided by x+1, the remainder is -12.
Answer provided by our tutors
if we divide p(x)=x^3-4x^2+ax-3 with (x+1) we get quotient x^2 - 5x + a + 5 and a reminder - a - 18 that is
x^3-4x^2+ax-3 = (x^2 - 5x + a + 5) (x+1) + (- a - 8)
from the condition in the text of the problem we have
- a - 8 = -12
a = 4