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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 $4x^2 + 3x - 2$?
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:
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 $b$?
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 $-x^2 + x + (4x^2 - x - 1)$?
What is the simplified form of the expression $-x^2 + x + (4x^2 - x - 1)$?
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What classification describes the resulting polynomial from simplifying $(8x^2 + 3x) - (12x^2 - 1)$?
What classification describes the resulting polynomial from simplifying $(8x^2 + 3x) - (12x^2 - 1)$?
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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:
-
- B
-
- A
-
- 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:
-
- A
-
- C
-
- 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.
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