Question

divide using long division. check your answer.\\((5x^2 - 2x + 2) \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

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

Step4: Divide new leading terms

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

Step5: Multiply divisor by $3$

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

Step6: Subtract to find remainder

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

Step7: Verify the result

$(x-1)(5x+3) + 5 = 5x^2 -5x +3x -3 +5 = 5x^2 -2x +2$

Answer:

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