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Polynomial
Division: Sections: Simplification and reduction, Polynomial long division There are two cases for dividing polynomials: either the "division" is really just a simplification and you're just reducting a fraction, or else you need to do long polynomial division (which is covered on the next page).
This is just a simplification problem, because there is only one term in the polynomial that you're dividing by. And, in this case, there is a common factor in the numerator (top) and denominator (bottom), so it's easy to reduce this fraction. There are two ways of proceeding. I can split the division into two fractions, each with only one term on top, and then reduce: ...or else I can factor out the common factor from the top and bottom, and then cancel off: Either way, the answer is the same: x + 2
Again, I can solve this in either of two ways: by splitting up the sum and simplifying each fraction separately: Copyright © Elizabeth Stapel 20002011 All Rights Reserved ...or else by taking the common factor out front and canceling it off: Either way, the answer is the same: 3x^{2} – 5x Note: Most books don't talk about the domain at this point. But if your book does, you will need to note, for the above simplification, that x cannot equal zero. That is, for the simplified form to be completely mathematically equal to the original expression, the solution would need to be "3x^{2} – 5x, for all x not equal to 0".
I can split the sum and reduce each fraction separately: The numerator (top) does indeed have a common factor; it's just a rather large one. Since both terms contain the factor "x + 3", then this is a common factor, and may be factored out front: Either way, the answer is the same: x – 2 Top  1  2  3  Return to Index Next >>



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