Add or subtract, as indicated. (5x2−4x+7)+(−4x2+3x−$$5)(5x^2-4x+7$$) + $$(-4x^2+3x-5)$$

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 23

Chapter 1, Problem 23

Add or subtract, as indicated. $(5 x^{2} - 4 x + 7) + (- 4 x^{2} + 3 x - 5)$

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Identify the polynomials to be added: $(5x^2 - 4x + 7)$ and $(-4x^2 + 3x - 5)$.

Remove the parentheses and write the expression as a sum of all terms: $5x^2 - 4x + 7 - 4x^2 + 3x - 5$.

Group like terms together. Like terms have the same variable raised to the same power: $(5x^2 - 4x^2) + (-4x + 3x) + (7 - 5)$.

Combine the coefficients of each group: For $x^2$ terms, add $5$ and $-4$; for $x$ terms, add $-4$ and $3$; for constants, add $7$ and $-5$.

Write the simplified polynomial by combining the results from the previous step, keeping the variable parts intact.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Addition and Subtraction

Adding or subtracting polynomials involves combining like terms, which are terms with the same variable raised to the same power. You add or subtract their coefficients while keeping the variable part unchanged. This process simplifies the expression into a single polynomial.

Like Terms

Like terms are terms in a polynomial that have identical variable parts, including the same exponents. For example, 5x² and -4x² are like terms because both have x raised to the second power. Recognizing like terms is essential for correctly combining polynomials.

Distributive Property

The distributive property allows you to multiply a term outside parentheses by each term inside. When subtracting polynomials, you distribute the negative sign across all terms in the second polynomial before combining like terms. This ensures correct addition or subtraction of coefficients.

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