SOLUTION: How do I solve the equation: 2u^4-5u^3-12u^2+2u-8 divided by u-4 ?

Question 31461: How do I solve the equation: 2u^4-5u^3-12u^2+2u-8 divided by u-4 ?
Answer by Cintchr(481) (Show Source): You can put this solution on YOUR website!

When dividing by a binomial you MUST make sure that the numerator is in decending order, and that there are no missing exponential values.
This numerator meets that criteria.
Now ... I have not found a way to show the long division in the rendering page so this may seem really long, but bear with me and we will take it all step by step.
FIRST: look at the denominator. you are going to divide by u first. Ask yourself: what number times u equals 2u^4? The answer: 2u^3
NEXT: multiply that value times the denominator
Subtract this value from the numerator ...
dont forget to distribute the negative

When you combine like terms ...

notice that the first term cancels. We did this on purpose.
continue on as we did in the the first step, this time asking: what number times u equals 3u^3? The answer: 3u^2
Multiply that value by the denominator.
subtract this answer once again.
watch the negatives
combine like terms.
notice that TWO terms will cancel in this step
back to step one:
What number times u equals 2u? The answer is 2.
Multiply it by the denominator.

Subtract this value from what remains.
watch the negatives ....
EVERYTHING cancels.
This means there is NO remainder.
Lets look at the numbers we came up with in each "First step" (the highlighted numbers)
and and
Add these numbers together
this is your answer

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