Algebraic Operations

The degree is the highest power present, and the leading coefficient is the number attached to it.

By the remainder theorem the answer is $f(2) = 8 + 8 - 5 = 11$.

$f(-3) = -27 + 18 + 15 - 6 = 0$. By the factor theorem a zero remainder means $(x+3)$ is a factor.

The factor theorem gives $f(1) = 0$: $2 + k - 7 + 2 = 0$, so $k = 3$.

$f(1) = 1 - 7 + 6 = 0$, so $(x-1)$ is a factor. Dividing gives $x^2 + x - 6 = (x+3)(x-2)$.

Let $x = 1$ to kill the $B$ term: $3 = 3A$, so $A = 1$. Let $x = -2$ to kill the $A$ term: $-18 = -3B$, so $B = 6$. Check: $(x+2) + 6(x-1) = 7x - 4$ ✓