Question

determine the quotient and remainder.
\\((x^2 - 12x + 32) \div (x - 8)\\)

Explanation:

Step1: Divide leading terms

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

Step2: Multiply divisor by $x$

$x(x-8) = x^2 - 8x$

Step3: Subtract from dividend

$(x^2 - 12x + 32) - (x^2 - 8x) = -4x + 32$

Step4: Divide new leading term

$\frac{-4x}{x} = -4$

Step5: Multiply divisor by $-4$

$-4(x-8) = -4x + 32$

Step6: Subtract to find remainder

$(-4x + 32) - (-4x + 32) = 0$

Answer:

Quotient: $x - 4$
Remainder: $0$