The binomial x-3 divides exactly the polynomial x^3-2x^2+cx-12 and c is a whole number then c is what?
To find the value of c, we can use the fact that if x - 3 is a factor of the polynomial x^3 - 2x^2 + cx - 12, then plugging in x = 3 should give us a remainder of 0.
So, substitute x = 3 into the polynomial:
(3)^3 - 2(3)^2 + c(3) - 12 = 0
27 - 18 + 3c - 12 = 0
Combine like terms:
3c - 3 = 0
3c = 3
Divide both sides by 3:
c = 1
Therefore, if x - 3 is a factor of the polynomial, c must be equal to 1.