Question

question 3
find the quotient and remainder using long division for: $\frac{2x^{3}-6x^{2}+7x-9}{2x^{2}+5}$
the quotient is
the remainder is
question help: video read written example

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

$(2x^3 - 6x^2 + 7x - 9) - (2x^3 + 5x) = -6x^2 + 2x - 9$

Step4: Divide new leading terms

$\frac{-6x^2}{2x^2} = -3$

Step5: Multiply divisor by $-3$

$-3(2x^2 + 5) = -6x^2 - 15$

Step6: Subtract to find remainder

$(-6x^2 + 2x - 9) - (-6x^2 - 15) = 2x + 6$

Answer:

The quotient is $x - 3$
The remainder is $2x + 6$