Question

question
use the long division method to find the result when $4x^3 + 25x^2 + 28x + 15$ is divided by $x + 5$.

Explanation:

Step1: Divide leading terms

$\frac{4x^3}{x} = 4x^2$
Multiply $x+5$ by $4x^2$: $4x^2(x+5)=4x^3+20x^2$
Subtract from dividend:
$(4x^3+25x^2+28x+15)-(4x^3+20x^2)=5x^2+28x+15$

Step2: Divide new leading terms

$\frac{5x^2}{x}=5x$
Multiply $x+5$ by $5x$: $5x(x+5)=5x^2+25x$
Subtract from current remainder:
$(5x^2+28x+15)-(5x^2+25x)=3x+15$

Step3: Divide new leading terms

$\frac{3x}{x}=3$
Multiply $x+5$ by $3$: $3(x+5)=3x+15$
Subtract from current remainder:
$(3x+15)-(3x+15)=0$

Answer:

$4x^2 + 5x + 3$