Question

If ( x+1) is a factor of a polynomial f(x) = x cube + k(x)squared + 3x + 10. Find the value of the constant k

Answer 1

HI,

Explanation:

If x+1 is a factor of f(x) then -1 is a zero of the polynomial f(x) and

`0=f(-1)=(-1)^3+k*(-1)^2-3+10=k+6\\\\k+6=0\\\\\boxed{k=-6}\\\\`

Answer 2

If (x+1) is a factor of f(x), it means that when we divide f(x) by (x+1), the remainder should be zero. Let's perform the division and find the value of the constant k.

By performing the division, we get:

f(x) = (x+1)(x^2 + (k-1)x + (k-3)) + (13-k)

For the remainder to be zero, we need (13-k) to be equal to zero. Therefore, k = 13.

So, the value of the constant k is 13.