Determine the value of k for which g(x) is a factor of f(x) of the following given polynomials :
`f(x)=x^(3)+2kx^(2)-11x+k-5andg(x)=2x+1`.

Determine the value of k for which g(x) is a factor of f(x) of the following given polynomials : f(x)=2x^(4)+3x^(3)-kx^(2)+x-6andg(x)=2x+3 .

Determine the value of k for which x-1 is a factor of (x^2 +1)+(x+k)dot

Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3dot

Using factor theorem, examine whether g(x) is a factor of f(x) of the following polynomials or not : f(x)=2x^(3)+10x^(2)-7x-456andg(x)=x-5 .

Using factor theorem, examine whether g(x) is a factor of f(x) of the following polynomials or not : f(x)=4x^(3)+x^(2)-20x-7andg(x)=3x+2

Using factor theorem, examine whether g(x) is a factor of f(x) of the following polynomials or not : f(x)=x^(4)-x-18andg(x)=x+2 .

Using factor theorem, examine whether g(x) is a factor of f(x) of the following polynomials or not : f(x)=x^(3)-7x^(2)+24x+162andg(x)=x+3

Determine whether (x + 1) is a factor of the follwing polynomials or not : x^(4)+x^(3)+x^(2)+4x+5

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

Find the value of k if (x - 2) is a factor of the polynomial (2x^(5)-6x^(4)-2kx^(3)+6kx^(2)+4kx+8) .