I'm not sure how well I can explain long division of polynomials without actually being able to write something for you.
Write this like a regular old division problem with (x + 2) on the outside and (2x^3 - x^2 + 3x - 1) under the bar.
To figure out what number goes on top... Just worry about the first term.
to get x to equal 2x^3, you multiply by 2x^2, so that's the first part of your answer.
Multiply (x + 2) by (2x^2) and subtract it from (2x^3 - x^2 + 3x - 1)
The first terms will cancel out, and you're left with - 5x^2 + 3x - 1.
Now do the same thing--only worry about the first term.
How do you get x to equal -5x^2? Multiply by (-5x). That's the second part of your answer. (which goes over the bar) then multiply (x + 2) by (-5x). You get (-5x^2 - 10). Subtract that from the main number you're still trying to get rid of.
Your new leading term is 13x.
How do you get rid of 13x?
Multiply by 13.
Subtract.
I ran off the edge of my paper, but I think you're left with 25.
You can't multiply x by any positive exponent to get 13, so 13 is your remainder.
That would make the answer (2x^2 - 5x + 13) + (25/(x +2))
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I'm not sure how well I can explain long division of polynomials without actually being able to write something for you.
Write this like a regular old division problem with (x + 2) on the outside and (2x^3 - x^2 + 3x - 1) under the bar.
To figure out what number goes on top... Just worry about the first term.
to get x to equal 2x^3, you multiply by 2x^2, so that's the first part of your answer.
Multiply (x + 2) by (2x^2) and subtract it from (2x^3 - x^2 + 3x - 1)
The first terms will cancel out, and you're left with - 5x^2 + 3x - 1.
Now do the same thing--only worry about the first term.
How do you get x to equal -5x^2? Multiply by (-5x). That's the second part of your answer. (which goes over the bar) then multiply (x + 2) by (-5x). You get (-5x^2 - 10). Subtract that from the main number you're still trying to get rid of.
Your new leading term is 13x.
How do you get rid of 13x?
Multiply by 13.
Subtract.
I ran off the edge of my paper, but I think you're left with 25.
You can't multiply x by any positive exponent to get 13, so 13 is your remainder.
That would make the answer (2x^2 - 5x + 13) + (25/(x +2))