Question

Could somebody please help me with this?

Answer 1

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.

Answer 2

2 is the solution for the equation to be 0

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

C = 3