Question

(5x³ + 54x² + 86x + 9) ÷ (5x + 9)

Explanation:

Step1: Polynomial long division setup

Divide $5x^3$ by $5x$:
$\frac{5x^3}{5x} = x^2$
Multiply $(5x+9)$ by $x^2$: $5x^3 + 9x^2$
Subtract from dividend:
$(5x^3 + 54x^2 + 86x + 9) - (5x^3 + 9x^2) = 45x^2 + 86x + 9$

Step2: Next term of quotient

Divide $45x^2$ by $5x$:
$\frac{45x^2}{5x} = 9x$
Multiply $(5x+9)$ by $9x$: $45x^2 + 81x$
Subtract from current remainder:
$(45x^2 + 86x + 9) - (45x^2 + 81x) = 5x + 9$

Step3: Final term of quotient

Divide $5x$ by $5x$:
$\frac{5x}{5x} = 1$
Multiply $(5x+9)$ by $1$: $5x + 9$
Subtract from current remainder:
$(5x + 9) - (5x + 9) = 0$

Answer:

$x^2 + 9x + 1$