Question

Perform the operations as described. Subtract $2 x^{2}-7 x-1$ from the sum of $x^{2}+9 x-4$ and $-5 x^{2}-7 x+10$

Name: Problem 41, Chapter 3: Intermediate Algebra
Uploaded: 2023-03-10T00:24:27-08:00
Duration: 2 min 21 s
Channel: Jennifer Stoner
Description: Perform the operations as described. Subtract 2 x^2-7 x-1 from the sum of x^2+9 x-4 and -5 x^2-7 x+10

   Perform the operations as described.
Subtract $2 x^{2}-7 x-1$ from the sum of $x^{2}+9 x-4$ and $-5 x^{2}-7 x+10$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 3, Problem 41

Instant Answer

Solved by Expert Jennifer Stoner

03/10/2023

Step 1

This is done by adding the corresponding terms of the polynomials together. \[ (x^{2}+9 x-4) + (-5 x^{2}-7 x+10) = (x^{2}-5 x^{2}) + (9 x-7 x) + (-4+10) = -4 x^{2} + 2 x + 6 \] Show more…

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Perform the operations as described. Subtract $2 x^{2}-7 x-1$ from the sum of $x^{2}+9 x-4$ and $-5 x^{2}-7 x+10$

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Key Concepts

Combining Like Terms

Combining like terms is the process of simplifying polynomial expressions by summing coefficients of terms that have the same variable raised to the same power. This concept is crucial for reducing expressions to their simplest form and is a key step in many algebraic operations.

Polynomial Subtraction

Polynomial subtraction involves subtracting one polynomial from another by distributing the subtraction (or negative sign) across the polynomial being subtracted and then combining like terms. This method is essential for manipulating algebraic expressions and solving equations.

Polynomial Addition

Polynomial addition is the process of combining two or more polynomials by adding the coefficients of corresponding like terms. This technique simplifies expressions and is a fundamental operation in algebra that helps in restructuring and solving polynomial equations.

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