Subtracting Polynomials

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Polynomials are expressions which can contain a single term, two terms, or more than two terms. Polynomials consist of constants, variables and their exponents and the terms are combined by adding, subtracting, multiplying or dividing. However there should not be division by a variable in a polynomial or there should not be a negative exponent on a variable. Subtracting polynomials is one of the operations performed on polynomials and the resultant answer is also a polynomial. While subtracting, it is important to combine only the like terms.
 
Example 1: Subtract the given two polynomials: (3x + 4 – 2x2) and (2x – 5 - 6x2).

Subtracting the given two polynomials, we get: (3x + 4 – 2x2) - (2x – 5 - 6x2)

Now we should first distribute the negative sign inside the parenthesis of the second polynomial, due to which the signs flip!

This gives: 3x + 4 – 2x2 – 2x + 5 + 6x2

Now we combine only the like terms, so bring them together.

3x – 2x + 4 + 5 – 2x2 + 6x2 _> x + 9 + 4x2 is the answer!
 
Example 2: Subtract the given two polynomials: (2x3 + 5x) and (x3 + 3x).

Subtracting the given two polynomials, we get: (2x3 + 5x) - (x3 + 3x).

Now we should first distribute the negative sign inside the parenthesis of the second polynomial, due to which the signs flip!

This gives: 2x3 + 5x – x3 – 3x

Now we combine only the like terms, so we can bring them together.

2x3 – x3 + 5x – 3x -> x3 + 2x is the answer!
 
 

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