Question

5.10 polynomial long division (my-opm-035)
score: 85/100 answered: 6/7
question 7
find the quotient and remainder using long division for
$\frac{2x^{3}-8x^{2}+7x-17}{2x^{2}+5}$
the quotient is
the remainder is

Explanation:

Step1: Divide leading terms

$\frac{2x^3}{2x^2} = x$

Step2: Multiply divisor by $x$

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

Step3: Subtract from dividend

$(2x^3 - 8x^2 + 7x - 17) - (2x^3 + 5x) = -8x^2 + 2x - 17$

Step4: Divide new leading terms

$\frac{-8x^2}{2x^2} = -4$

Step5: Multiply divisor by $-4$

$-4(2x^2 + 5) = -8x^2 - 20$

Step6: Subtract to find remainder

$(-8x^2 + 2x - 17) - (-8x^2 - 20) = 2x + 3$

Answer:

The quotient is $x - 4$
The remainder is $2x + 3$