Question

Given that (x+6) is a factor of f(x)=x^3+3x^2+3x+k

Answer 1

given that (x+6) is a factor of f(x)=x^3+3x^2+3x+k

If (x+6) is a factor

that means

For x=-6 ------> f(-6)=0

substitute the value of x and solve for k

so

0=(-6)^3+3(-6)^2+3(-6)+k

solve for k

0=-216+108-18+k

0=-126+k

k=126