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Chapter 5: Problem 112

Explain how to add polynomials.

Short Answer

Expert verified
Adding polynomials involves combining like terms from each polynomial to result in a single polynomial. The result, when the polynomials \(4x^{2} + 3x - 2\) and \(2x^{2} - x + 5\) are added, is \(6x^{2} + 2x + 3\).

Step by step solution

01

Identify Like Terms

Firstly, find the terms in each polynomial that are similar. These are the terms that have exactly the same variables raised to the same powers. For instance, in the polynomials \(4x^{2} + 3x - 2\) and \(2x^{2} - x + 5\), the like terms are \(4x^{2}\) and \(2x^{2}\), \(3x\) and \(-x\) as well as \(-2\) and \(5\).
02

Add Like Terms

After determining the like terms in each polynomial, the next step is to add the coefficients of these like terms together. The coefficient of a term is the number in front of the variable. In the example given above, When you add the like terms, you get \(4x^{2} + 2x^{2} = 6x^{2}\), \(3x - x =2x\) and \(-2 + 5 =3\). Therefore, the sum of the polynomials is \(6x^{2} + 2x + 3\).
03

Check the result

Ensure that the result is in standard form which means the terms are written from highest power to lowest power of the variable. Also, ensure that no like terms are left to be combined.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(y-1)\left(y^{2}+y+1\right)=y^{3}-1$$

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