Question

use the long division method to find the result when $3x^3 + 16x^2 + 22x + 4$ is divided by $x + 2$.

Explanation:

Step1: Divide leading terms

$\frac{3x^3}{x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(x+2) = 3x^3 + 6x^2$
Subtract from dividend:
$(3x^3 + 16x^2 + 22x + 4) - (3x^3 + 6x^2) = 10x^2 + 22x + 4$

Step2: Divide new leading terms

$\frac{10x^2}{x} = 10x$
Multiply divisor by $10x$: $10x(x+2) = 10x^2 + 20x$
Subtract from current polynomial:
$(10x^2 + 22x + 4) - (10x^2 + 20x) = 2x + 4$

Step3: Divide final leading terms

$\frac{2x}{x} = 2$
Multiply divisor by $2$: $2(x+2) = 2x + 4$
Subtract from current polynomial:
$(2x + 4) - (2x + 4) = 0$

Answer:

$3x^2 + 10x + 2$