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

1 Answer
Dwight
Dec 31, 2016

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.

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