Question

Determine the polynomial to be placed in the shaded area to give a true statement. $$ \overline{3 x+2}=x-3 $$

Name: Problem 80, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2021-05-14T17:42:59-08:00
Duration: 1 min 16 s
Channel: Robert Daugherty
Description: Determine the polynomial to be placed in the shaded area to give a true statement. 3 x+2=x-3

   Determine the polynomial to be placed in the shaded area to give a true statement.
$$
\overline{3 x+2}=x-3
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 80

Instant Answer

Solved by Expert Robert Daugherty

05/14/2021

Step 1

Since the absolute value of a number is always positive, we have two cases: 1) If the expression inside the absolute value is positive or zero, then the absolute value is equal to the expression itself: $$ 3x + 2 = x - 3 $$ 2) If the expression inside the Show more…

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Determine the polynomial to be placed in the shaded area to give a true statement. $$ \overline{3 x+2}=x-3 $$

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Key Concepts

Combining Like Terms

This process involves grouping and summing terms in an expression that have the same variable raised to the same exponent. It is a key step in simplifying polynomial expressions and is crucial when isolating and solving for a missing component in a polynomial equation.

Polynomial Addition/Subtraction

This concept involves adding or subtracting polynomials by combining like terms. It is fundamental when determining a missing polynomial in an identity or equation, as it allows for the systematic combination of similar power terms to simplify or manipulate expressions.

Polynomial Identities and Equating Coefficients

For two polynomials to be equal, each corresponding coefficient must match. This principle is used to solve for unknown polynomials by setting up equations that equate the coefficients of like powers, ensuring the equality holds for all variable values.

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