Q: (2x + 6x³ + 5) ÷ (2x² + 4)
A: OK, as I tried to do in my previous polynomial long division example, I will try to format this like a “long division” problem the best I can
First, I will re-arrange to get: (6x³ + 2x + 5) ÷ (2x² + 4)
2x² + 4 | 6x³ + 2x + 5
Ok, we start by asking: How many times does 2x² go into 6x³? The answer: 3x… Which goes about the “long division problem”:
………….. 3x
2x² + 4 | 6x³ + 2x + 5
Now, we multiply 3x by both 2x² and +4. This then will get carried down in teal like so:
………….. 3x
2x² + 4 | 6x³ + 2x + 5
……………6x³ + 12x
Now, we subtract the teal from the red:
………….. 3x
2x² + 4 | 6x³ + 2x + 5
………….-(6x³ + 12x)
…………………..--10x + 5
Now, since 2x² cannot go into -10x, we are done.
Our answer is 3x + (-10x + 5)/(2x² + 4)
Another way of saying this is: 3x is the quotient and -10x + 5 is the remainder.