Polynomial Functions Math Example 3

Solution

1. 1
   Divide $2x^3$ by $x$: get $2x^2$. Multiply: $2x^2(x + 2) = 2x^3 + 4x^2$. Subtract: $(2x^3 + 3x^2) - (2x^3 + 4x^2) = -x^2$.
2. 2
   Bring down $-5x$: $-x^2 - 5x$. Divide $-x^2$ by $x$: get $-x$. Multiply: $-x(x + 2) = -x^2 - 2x$. Subtract: $(-x^2 - 5x) - (-x^2 - 2x) = -3x$.
3. 3
   Bring down $+1$: $-3x + 1$. Divide $-3x$ by $x$: get $-3$. Multiply: $-3(x + 2) = -3x - 6$. Subtract: $(-3x + 1) - (-3x - 6) = 7$.
4. 4
   Result: $2x^2 - x - 3 + \frac{7}{x + 2}$.