#Question on Polynomial Long Divison

3 messages · Page 1 of 1 (latest)

rustic obsidian
#

Hey so I’m currently trying to solve the problem (8x^4-5)/(2x+1) and I got my final solution being 4x^3-2x^2+x-(1/2) with a remainder of 4 and a fraction of (1/2) but when I went to check on mathaway the result of the division had the exact same solution but with a remainder of 9? And then another with a remainder of -(9/2)? So I was wondering, can a polynomial have a fraction in its remainder or not as this problem confuses me alot and there’s no step solution to guide me through

half gullBOT
solid trench
#

If we take $$(8x^4-5)/(2x+1) = 4x^3-2x^2+x-1/2-4.5/2x+1$$
$$ -(8x^4+4x^3) $$
$$ -4x^3-5 $$
$$ -(-4x^2-2x^2) $$
$$ 2x^2-5 $$
$$ -(2x^2+x) $$
$$ -x-5 $$
$$ -(-x-1/2) $$
$$ -4.5 $$
$$ -(-4.5) $$
$$ 0 $$

It simplifies -4.5 as -9/2 and therefore:
$$ -4.5/2x+1 = -9/(2(2x+1))$$
so
$$ (8x^4-5)/(2x+1) = 4x^3-2x^2+x-1/2-4.5/2x+1 $$
$$= 4x^3-2x^2+x-1/2-9/(2(2x+1))$$