Question

What value of k makes the factor (x-3)a factor of the function, f(x)=3x^(3)-10x^(2)+x+k

a.0

b.14

c.6

d.-36

e.-130

Answer 1

C. 6

Explanation:

If x-3 is a factor of the polynomial f(x)=3x^(3)-10x^(2)+x+k, then x = 3 is one of the zeros of the polynomial.

Let p(x) = 0 where x = 3

Substitute this values into the polynomial

0 =3(3)^(3)-10(3)^(2)+3+k

0 = 3^4-10(9)+3+k

0 = 81-90+3+k

0 = -9+3+k

0 = -6+k

k -6 = 0

k = 6

Hence the value of k is 6