Question

Consider the polynomial P(x)=x³+kx²+x+6.Find the value of k so that x+1 is a factor of P.

Answer 1

The value of k will be -4

Explanation:

We have given polynomial
`P(X)=x^3+kx^2+x+6`

It is given that x+1 is factor of the polynomial

And we have to find the value of k

As x+1 is the factor of polynomial so x+1 = 0 that is x = -1 will be the root of polynomial

So if we put x = -1 in the polynomial then the p(-1) will be zero

So
`0=(-1)^3+k(-1)^2-1+6`

`k=-4`

So the value of k will be -4