Question

find the quotient and remainder using long division for $\frac{x^2 + 6x + 17}{x + 3}$.
the quotient is
the remainder is

Explanation:

Step1: Divide leading terms

$\frac{x^2}{x} = x$

Step2: Multiply divisor by $x$

$x(x+3) = x^2 + 3x$

Step3: Subtract from dividend

$(x^2 + 6x + 17) - (x^2 + 3x) = 3x + 17$

Step4: Divide new leading terms

$\frac{3x}{x} = 3$

Step5: Multiply divisor by 3

$3(x+3) = 3x + 9$

Step6: Subtract to find remainder

$(3x + 17) - (3x + 9) = 8$

Answer:

The quotient is $x + 3$
The remainder is $8$