Question

Find the value of c so that the polynomial p(x) is divisible by (x-3).
p(x) = -x^3+cx^2-4x+3

Answer 1

c=4

Explanation:

If polynomial p(x) is divisible by (x-3), then x=3 is zero of p(x).

p(x) =-x^3+cx^2-4x+3

0=p(3)=-3^3 +c*3^2 - 4*3+3

0=-27+9c-12+3

0=-27-9+9c

0=-36+9c

36=9c

c=36/9

c=4