Question

$$(5x^2 - 2x + 3) div (x - 1)$$ the quotient is \\(\square\\) with remainder \\(\square\\).

Explanation:

Step1: Divide leading terms

$\frac{5x^2}{x} = 5x$

Step2: Multiply divisor by $5x$

$5x(x-1) = 5x^2 - 5x$

Step3: Subtract from dividend

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

Step4: Divide new leading terms

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

Step5: Multiply divisor by 3

$3(x-1) = 3x - 3$

Step6: Subtract to find remainder

$(3x + 3) - (3x - 3) = 6$

Answer:

The quotient is $5x + 3$ with remainder $6$.