Question

Could somebody please help me with this?

Answer 1

2 is the solution for the equation to be 0

Plug 2 into the equation you will get the value of C.

C = 3

Answer 2

For this problem, we are going to use the Remainder Theorem. This says that for
`x - n` to be a factor of a polynomial
`p(x)`, then
`p(n) = 0`. Essentially, it says that
`x - n` is a factor if when you substitute
`n` into the polynomial you get a result of 0.

Thus, in our case, when we substitute
`x = 2` into the polynomial, we should get an answer of 0 if
`x - 2` is a factor of the polynomial. Given this information, we can solve for
`c`:

`p(2) = 2^3 - 4(2^2) + 2c + 2 = 0`

`8 - 16 + 2c + 2 = 0`

`2c - 6 = 0`

`2c = 6`

`c = 3`

The solution is c = 3.