Question

For what value of k, –4 is a zero of the polynomial x² – x – (2k + 2)?

Answer 1

We know that if  x = a is zero polynomial then x – 2 is a factor of f(x)

Since –4 is zero of f(x)

Therefore x + 4 is a factor of f(x)

Now, we divide `f(x)= x^2 -x -(2k + 2)` by  `g(x)= x+ 2` to find the value of k 

                      x – 5
`x + 4")"overline(+ \cancel(x^2) - x - 2k - 2)`
          `+ \cancel(x^2) + 4x`
           –        –       
                    `- \cancel(5x) - 2k - 2`
                    `- \cancel(5x)            -20`
                    +                 +      
                                –2k + 18

Now, Remainder = 0

` -2k + 18 =0`

` - 2k = -18`

` k = (-18)/(-2)`

`k = (cancel(-)18)/(cancel(-)2)`

k = 9 

Hence, the value of k is 9.