SOLUTION: 4x^4-10x^3+8x^2 ___________ ___ 2x Thank you, I am really confused.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 4x^4-10x^3+8x^2 ___________ ___ 2x Thank you, I am really confused.      Log On


   

Question 181838This question is from textbook
: 4x^4-10x^3+8x^2
_______________
2x
Thank you, I am really confused. This question is from textbook

Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
You start out with:
.
%284x%5E4-10x%5E3%2B8x%5E2%29%2F2x
.
Notice, each term in the numerator is divisible by 2. So, factor out a 2:
%282%282x%5E4-5x%5E3%2B4x%5E2%29%29%2F2x
.
At this point you can cancel the 2 in the numerator and the 2 in the denominator leaving:
%282x%5E4-5x%5E3%2B4x%5E2%29%2Fx
.
Now, notice each term in the numerator is divisible by x. So, factor out an x:
%28x%282x%5E3-5x%5E2%2B4x%29%29%2Fx
.
At this point you can cancel the x in the numerator and the x in the denominator leaving:
2x%5E3-5x%5E2%2B4x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E4-10x%5E3%2B8x%5E2%29%2F%282x%29 Start with the given expression


%282x%5E2%282x%5E2-5x%2B4%29%29%2F%282x%29 Factor out the GCF 2x%5E2


%282x%2Ax%282x%5E2-5x%2B4%29%29%2F%282x%29 Break down 2x%5E2 into 2x%2Ax


%28highlight%282x%29%2Ax%282x%5E2-5x%2B4%29%29%2Fhighlight%282x%29 Highlight the common terms.


%28cross%282x%29%2Ax%282x%5E2-5x%2B4%29%29%2Fcross%282x%29 Cancel out the common terms.


x%282x%5E2-5x%2B4%29 Simplify (by removing the canceled terms)


2x%5E3-5x%5E2%2B4x Distribute


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Answer:

So %284x%5E4-10x%5E3%2B8x%5E2%29%2F%282x%29 simplifies to 2x%5E3-5x%5E2%2B4x


In other words, %284x%5E4-10x%5E3%2B8x%5E2%29%2F%282x%29=2x%5E3-5x%5E2%2B4x where x%3C%3E0