-3x^4 + kx^3 -7x^2-11x+5; x-5

Question

find the value of k so that the second expression is a factor of the first.

Answer 1

The polynomial f (x ) = - 3x ^4 + k x ^3 - 7x ^2- 11x  + 5

x - 5 is a factor of f (x )

By the factor theorm if  f ( c ) = 0 then ( x - c ) is a factor.

So f ( 5 ) = 0.

-3 (5^4 ) + k (5^3) - 7(5^2) -11 (5) + 5 = 0

-3 (625) + k ( 125 ) -7 (25) - 11 (5) + 5 = 0

-1875 + k ( 125 ) - 175 - 55 + 5 = 0

- 2100 + k ( 125 ) = 0

k ( 125 ) = 2100

k  = 2100 / 125

k = 84 / 5.

The value of  the k = 84 / 5.