16x^4 - 81 divided by 2x - 3?

Question

thanks a lot in advanced

i forgot to mention you have to use long division to solve this problem.

Answer 1

8x^3 + 12x^2 + 18x + 27

Now..... I suggest you get your butt in gear and figure out how to work these --before-- your next test ☺

Doug

Answer 2

16x^4-81=(4x^2+9)(2x+3)(2x-3) divided by 2x-3 cancels out

(4x^2+9)(2x+3)
8x^3+12x^2+18x+27

Answer 3

16x^4 - 81 is factorable, it is a difference of two squares.
(4x^2 - 9)(4x^2 +9)

4x^2 - 9 is factorable as well, and it is also a difference of two squares:
(2x - 3)(2x + 3)

so you have: (4x^2 +9)(2x - 3)(2x +3)/(2x-3)

cross out the 2x -3 and your answer is:
(4x^2 + 9)(2x +3)

Answer 4

Apply formula a^2 - b^2 = (a - b)(a + b) twice.
(4x^2)^2 - 9^2 = (4x^2 - 9)(4x^2 + 9) = (2x - 3)(2x+3)(4x^2 + 9)
Divide by (2x-3) and you get (2x+3)(4x^2 + 9).