How do I do (x^3 - 4)/(2x + 5)?

I like to use long division. Don't forget to leave place holders for your x² and x terms with coefficients of zero:

. . . . . _(1/2)x²_-_(5/4)x_+_(25/8)_________

2x + 5 ) x³ + 0x² + 0x - 4

. . . . . . x³ + (5/2)x²

. . . . --------------------

. . . . . . . -(5/2)x² + 0x - 4

. . . . . . . -(5/2)x² - (25/4)x

. . . . . . ---------------------------

. . . . . . . . . . . . . (25/4)x - 4

. . . . . . . . . . . . . (25/4)x + (125/8)

. . . . . . . . . . . -------------------------------

. . . . . . . . . . . . . . . . -4 - 125/8

So first, let's simplify that remainder:

-32/8 - 125/8

-157/8

Put the remainder over the divisor:

(-157/8) / (2x + 5)

change it to multiplication of the reciprocal:

(-157/8) * 1 / (2x + 5)

and simplify:

-157 / (16x + 40)

Now add that to the quotient that we calculated:

(1/2)x² - (5/4)x + (25/8) - 157 / (16x + 40)

Using long division:

(x³-4) ÷ (2x+5) = 0.5x² - 1.25x + 3.125 remainder -19.625

https://www.flickr.com/photos/dwread/26213521464/i...