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Given two polynomials, their sum or difference can be calculated. Consider the following pair of polynomials. - 2x^2 + x + 3 and 2x^2 + 4x - 10 In order to add these polynomials, there are three steps to follow. Note that subtraction of the polynomials can be performed by applying the same three steps, only instead of adding the like terms, they will be subtracted.
Remove parentheses
Commutative Property of Addition
When subtracting polynomials, remember to distribute - 1 to the terms of the second polynomial before rearranging the terms.
Remove parentheses
Distribute - 1
Commutative Property of Addition
Therefore, the sum is 5x-7. Note that the given polynomials are of degree 2. However, the new polynomial is of degree 1 because the x^2-terms canceled each other out. If they had not canceled each other out, the new polynomial would have also been of degree 2.
When adding or subtracting two polynomials of degrees m and n, the degree of the resulting polynomial is at most the equal to the degree of higher degree polynomial.