Algebra 2 Study Questions

Questions and Answers

What is the other trinomial if the sum of two trinomials is $6x^2 - 5x + 4$ and one of the trinomials is $4x^2 + 3x - 2$?

2x^2 - 8x + 6

Match the expressions with the correct letters:

-9x^2 - 2x + 7 = A Another expression = B Yet another expression = C

Which of the following statements is true regarding the polynomial $p(x)$ and an integer $b$?

The difference of $p(x)$ and $b$ is not a polynomial.

The sum of $p(x)$ and $b$ is not a polynomial.

The sum and difference of $p(x)$ and $b$ are polynomials. (correct)

Both the sum and difference of $p(x)$ and $b$ are not polynomials.

What is the simplified form of the expression $-x^2 + x + (4x^2 - x - 1)$?

<p>3x^2 - 1</p> Signup and view all the answers

What classification describes the resulting polynomial from simplifying $(8x^2 + 3x) - (12x^2 - 1)$?

<p>Quadratic Trinomial</p> Signup and view all the answers

Study Notes

Trinomials and Their Sums

The sum of two trinomials yields 6x² - 5x + 4.
Given trinomial: 4x² + 3x - 2.
The other trinomial must be 2x² - 8x + 6.

Expression Comparisons

When comparing expressions like -9x² - 2x + 7, answer choices need to be identified by letter.
Responses for which letter corresponds to which expression include:
- 1. B
- 1. A
- 1. C

Polynomials and Integers

For polynomials like p(x), adding or subtracting an integer (b) results in another polynomial.
Conclusion: both the sum and difference remain polynomials.

Expression Simplification

A complex expression simplifies efficiently to 6x² + 5x - 4/15.
Representation of polynomial expressions can vary and should be checked for correctness.

Resulting Polynomial Classification

Simplifying (8x² + 3x) - (12x² - 1) results in a quadratic trinomial.
Polynomial types include quadratic, cubic, etc., classified by the highest degree.

Additional Expression Comparisons

In another expression set (similar to prior), for -7x² - 2x + 5, correct letter assignments are necessary.
Letter assignments include:
- 1. A
- 1. C
- 1. B

Simplification of Multiple Terms

The expression (-x² + x) + (4x² - x - 1) simplifies neatly to 3x² - 1.
Careful combining and simplifying is crucial for accuracy.

Description

Test your knowledge with these Algebra 2 study questions. This quiz features various problems involving trinomials, expressions, and polynomials, designed to enhance your understanding of algebraic concepts. Perfect for review or preparation for exams!