Question

question
use the long division method to find the result when $3x^3 + 16x^2 + 30x + 21$ is divided by $3x + 7$.

Explanation:

Step1: Divide leading terms

$\frac{3x^3}{3x} = x^2$
Multiply divisor by $x^2$: $(3x+7)x^2 = 3x^3+7x^2$
Subtract from dividend:
$(3x^3+16x^2+30x+21)-(3x^3+7x^2) = 9x^2+30x+21$

Step2: Divide new leading terms

$\frac{9x^2}{3x} = 3x$
Multiply divisor by $3x$: $(3x+7)(3x) = 9x^2+21x$
Subtract:
$(9x^2+30x+21)-(9x^2+21x) = 9x+21$

Step3: Divide final leading terms

$\frac{9x}{3x} = 3$
Multiply divisor by $3$: $(3x+7)(3) = 9x+21$
Subtract:
$(9x+21)-(9x+21) = 0$

Answer:

$x^2 + 3x + 3$