Question

Perform the indicated operations. $$ \left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right) $$

Name: Problem 52, Chapter 3: Intermediate Algebra
Uploaded: 2023-03-10T04:09:15-08:00
Duration: 1 min 32 s
Channel: Nick Johnson
Description: Perform the indicated operations. (5 x^2+x+4)+(-x^2+2 x+4)+(-14 x^2-x+6)

   Perform the indicated operations.
$$
\left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right)
$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 3, Problem 52

Instant Answer

Solved by Expert Nick Johnson

03/10/2023

Step 1

Since there are no negative signs in front of the parentheses, we can simply drop them: $$ 5x^{2}+x+4-x^{2}+2x+4-14x^{2}-x+6 $$ Show more…

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Perform the indicated operations. $$ \left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right) $$

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Key Concepts

Associative and Commutative Properties

These properties allow us to rearrange and group terms in an addition operation without changing the result. They are essential for simplifying and combining like terms in polynomial operations.

Polynomial

A polynomial is an expression made up of variables and coefficients, using operations such as addition, subtraction, and multiplication, with the variables raised to non-negative integer exponents. Polynomials form the backbone of algebra and are used in various mathematical contexts.

Like Terms

Like terms in an expression are terms that have the same variables raised to the same powers. This similarity allows their coefficients to be added or subtracted together during the process of simplifying the expression.

Adding Polynomials

Polynomial addition involves combining two or more polynomials by adding the coefficients of like terms. This process simplifies the expression and is fundamental in algebraic operations.

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