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Questions and Answers
What is the primary rule to remember when adding polynomials?
What is the primary rule to remember when adding polynomials?
- Multiply the coefficients and add the exponents.
- Distribute the negative sign across all terms.
- Only add the like terms. (correct)
- Add all coefficients, regardless of the variable.
When subtracting one polynomial from another, what initial step is crucial before combining like terms?
When subtracting one polynomial from another, what initial step is crucial before combining like terms?
- Multiply the two polynomials together.
- Add a constant to both polynomials.
- Factor each polynomial completely.
- Distribute the negative sign to each term of the polynomial being subtracted. (correct)
What operation is performed on the exponents when multiplying polynomials?
What operation is performed on the exponents when multiplying polynomials?
- Exponents remain the same.
- Exponents are multiplied.
- Exponents are added. (correct)
- Exponents are subtracted.
What is the result of $(2x^7 + 5) * 3x$?
What is the result of $(2x^7 + 5) * 3x$?
Simplify: $(4x + 9)(4x - 9)$
Simplify: $(4x + 9)(4x - 9)$
When adding or subtracting polynomials, what must be true of the terms being combined?
When adding or subtracting polynomials, what must be true of the terms being combined?
Which expression represents the result of subtracting $(2x^2 - 5x + 3)$ from $(7x^2 + 2x - 1)$?
Which expression represents the result of subtracting $(2x^2 - 5x + 3)$ from $(7x^2 + 2x - 1)$?
If you are given two polynomials, $P(x) = 4x^3 - 2x + 1$ and $Q(x) = x^2 + 3x - 5$, what is $P(x) + Q(x)$?
If you are given two polynomials, $P(x) = 4x^3 - 2x + 1$ and $Q(x) = x^2 + 3x - 5$, what is $P(x) + Q(x)$?
Determine the product of the polynomials $(x+3)$ and $(x^2 - 2x + 1)$.
Determine the product of the polynomials $(x+3)$ and $(x^2 - 2x + 1)$.
What is the result of subtracting $(3x^3 - x + 5)$ from $(5x^3 + 4x - 2)$?
What is the result of subtracting $(3x^3 - x + 5)$ from $(5x^3 + 4x - 2)$?
Flashcards
Adding Polynomials
Adding Polynomials
When adding polynomials, combine only like terms.
Subtracting Polynomials
Subtracting Polynomials
Distribute the negative sign to each term in the second polynomial, then add.
Multiplying Polynomials
Multiplying Polynomials
Multiply the coefficients and add the exponents of like variables.
Difference of Squares
Difference of Squares
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Study Notes
- 2025 IT Math Study Guide
- A-SSE: Seeing Structure in Expressions
- A-APR: Arithmetic with Polynomials
Addition and Subtraction
- When adding polynomials, combine only like terms.
- Example: (3x⁴ - 2x + 7) + (5x⁴ + 3x³ - 4) = 8x⁴ + 3x³ - 2x + 3
- When subtracting, distribute the negative sign to the second polynomial, then add.
- Example: (8x⁴ + 3x³ - 2x + 3) - (5x⁴ + 3x³ - 4) = 3x⁴ + 0x³ - 2x + 7 or 3x⁴ - 2x + 7
Multiplication
- When multiplying, multiply the coefficients and add the exponents.
- Examples:
- 3x * (2x⁷ + 5) = 6x⁸ + 15x
- (4x + 9)(4x - 9) = 16x² + 0x - 81 or 16x² - 81
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