Question

How do you divide `(2x ^ { 2} - 5x + 7) \div ( 2x - 1)`?

Answer 1

You divide in a manner similar to long division. See the explanation.

Explanation:

Basically, you plan to find terms that will cause the dividend to make the divisor `2x^2-5x+7` "disappear" one term at a time, starting with the highest order in `x`.

It's best to show you how:

If you multiply `2x-1` by `x`, you will get `2x^2-2x`
If you subtract this from the original divisor `2x^2-5x+7`, the term in `x^2` will disappear. Therefore, `x` is the leftmost term in your answer.

Do the subtraction
`(2x^2-5x+7)-(2x^2-2x)` = `-3x+7`

Now repeat this process, this time arranging for the `-3x` term to disappear in the subtraction. This requires you multiply `2x-1` by `-1.5`. You will get `-3x+1.5`. So, -1.5 is the next term in the answer.

Do the subtraction
`-3x+7 - (-3x+1.5)= 5.5`

The answer is `x-1.5` with a remainder of 5.5.