Question

divide using long division. check your answer.
\\((5x^2 - 7x + 1) \div (x - 2)\\)

the quotient is \\(\square\\) with remainder \\(\square\\).

Explanation:

Step1: Divide leading terms

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

Step2: Multiply divisor by result

$5x(x-2) = 5x^2 - 10x$

Step3: Subtract from dividend

$(5x^2 -7x +1) - (5x^2 -10x) = 3x +1$

Step4: Divide new leading term

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

Step5: Multiply divisor by result

$3(x-2) = 3x -6$

Step6: Subtract to find remainder

$(3x +1) - (3x -6) = 7$

Step7: Verify the result

$(x-2)(5x+3) +7 = 5x^2-10x+3x-6+7 = 5x^2-7x+1$

Answer:

The quotient is $5x+3$ with remainder $7$.