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 result

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

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 result

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

Step6: Subtract to get remainder

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

Answer:

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