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Questions and Answers
What is the first step in adding polynomials?
What is the first step in adding polynomials?
- Combine terms with different variables and exponents
- Subtract the coefficients of the polynomials
- Add the coefficients of the polynomials
- Combine terms with the same variable(s) and exponent(s) (correct)
What is the result of adding $(2x^2 + 3x - 1)$ and $(x^2 - 2x - 3)$?
What is the result of adding $(2x^2 + 3x - 1)$ and $(x^2 - 2x - 3)$?
- $3x^2 + x - 4$ (correct)
- $2x^2 + x^2 + x - 4$
- $3x^2 + 5x - 2$
- $x^2 + 2x + 2$
How do you subtract polynomials?
How do you subtract polynomials?
- Combine unlike terms and subtract coefficients
- Combine like terms and add coefficients
- Combine like terms and subtract coefficients (correct)
- Combine unlike terms and add coefficients
What is the result of subtracting $(x^2 - 2x - 3)$ from $(2x^2 + 3x - 1)$?
What is the result of subtracting $(x^2 - 2x - 3)$ from $(2x^2 + 3x - 1)$?
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What is the purpose of combining like terms in polynomial operations?
What is the purpose of combining like terms in polynomial operations?
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Study Notes
Polynomial Operations
Adding Polynomials
- To add polynomials, combine like terms:
- Combine terms with the same variable(s) and exponent(s)
- Add the coefficients of the like terms
- Example: (2x2+3x−1)+(x2−2x−3)=(2x2+x2)+(3x−2x)+(−1−3)=3x2+x−4(2x^2 + 3x - 1) + (x^2 - 2x - 3) = (2x^2 + x^2) + (3x - 2x) + (-1 - 3) = 3x^2 + x - 4(2x2+3x−1)+(x2−2x−3)=(2x2+x2)+(3x−2x)+(−1−3)=3x2+x−4
Subtracting Polynomials
- To subtract polynomials, combine like terms:
- Change the sign of the terms in the second polynomial (i.e., subtract)
- Combine terms with the same variable(s) and exponent(s)
- Add the coefficients of the like terms
- Example: (2x2+3x−1)−(x2−2x−3)=(2x2−x2)+(3x+2x)+(−1+3)=x2+5x+2(2x^2 + 3x - 1) - (x^2 - 2x - 3) = (2x^2 - x^2) + (3x + 2x) + (-1 + 3) = x^2 + 5x + 2(2x2+3x−1)−(x2−2x−3)=(2x2−x2)+(3x+2x)+(−1+3)=x2+5x+2
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Description
Learn how to add and subtract polynomials by combining like terms, including changing the sign of terms when subtracting. Practice with examples to become proficient in polynomial operations.
