Question

find the quotient and remainder using long division for: $\frac{x^{2}+8x+23}{x+3}$.
the quotient is
the remainder is
question help: video 1 video 2 read 1 written example 1

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

$(x^2 + 8x + 23) - (x^2 + 3x) = 5x + 23$

Step4: Divide new leading terms

$\frac{5x}{x} = 5$

Step5: Multiply divisor by 5

$5(x+3) = 5x + 15$

Step6: Subtract to find remainder

$(5x + 23) - (5x + 15) = 8$

Answer:

The quotient is $x + 5$
The remainder is $8$