Questions and Answers
What is the difference of the polynomials $(-2x^3y^2 + 4x^2y^3 - 3xy^4) - (6x^4y - 5x^2y^3 - y^5)$?
-6x^4y - 2x^3y^2 + 9x^2y^3 - 3xy^4 + y^5
Which expression represents the total perimeter of her sandwich, and if $x = 1.2$, what is the approximate length of the crust?
8x^2 + 34; 45.52 centimeters
What is the sum of the polynomials $(7x^3 - 4x^2) + (2x^3 - 4x^2)$?
9x^3
If the sum of two polynomials is $8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9$ and one addend is $2d^5 - c^3d^2 + 8cd^4 + 1$, what is the other addend?
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What is the profit if the revenue is modeled by $3x^2 + 180x$ and the cost by $3x^2 - 160x + 300$, with $x$ representing the number of televisions sold? If 150 televisions are sold, what is the profit?
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What expression represents the profit if the revenue for toy cars is modeled by $3x^2 + 4x - 60$ and the cost by $3x^2 - x + 200$?
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What is the additive inverse of the polynomial $-9xy^2 + 6x^2y - 5x^3$?
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The sum of the two polynomials $6s^2t - 2st^2$ and $4s^2t - 3st^2$ is a binomial with a degree of 3.
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What is the sum of the polynomials $(-x^2 + 9) + (-3x^2 - 11x + 4)$?
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What is true about the degree of the sum and difference of the polynomials $3x^5y - 2x^3y^4 - 7xy^3$ and $-8x^5y + 2x^3y^4 + xy^3$?
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Study Notes
Adding and Subtracting Polynomials
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The difference of the polynomials (-2x³y² + 4x²y³ - 3xy⁴) and (6x⁴y - 5x²y³ - y⁵) is -6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵.
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The expression for the total perimeter of a sandwich, represented as 8x² + 34, gives a crust length of approximately 45.52 centimeters when x = 1.2.
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The sum of (7x³ - 4x²) and (2x³ - 4x²) results in 9x³.
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Given the sum 8d⁵ - 3c³d² + 5c²d³ - 4cd⁴ + 9, if one addend is 2d⁵ - c³d² + 8cd⁴ + 1, the other addend is 6d⁵ - 2c³d² - 3c²d³ - 4cd⁴ + 8.
Profit Calculation using Polynomials
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Revenue for a television manufacturing company is modeled by 3x² + 180x and cost by 3x² - 160x + 300, resulting in a profit of $50,700 when 150 televisions are sold.
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For a toy car manufacturing company, revenue is represented by 3x² + 4x - 60, and cost by 3x² - x + 200; therefore, the profit expression is 5x - 260.
Additive Inverses and Polynomial Properties
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The additive inverse of the polynomial -9xy² + 6x²y - 5x³ is 9xy² - 6x²y + 5x³.
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The sum of the polynomials 6s²t - 2st² and 4s²t - 3st² results in a binomial with a degree of 3.
Summing and Differencing Polynomials
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The sum of the polynomials (-x² + 9) and (-3x² - 11x + 4) simplifies to -4x² - 11x + 13.
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The degree of the sum of the polynomials 3x⁵y - 2x³y⁴ - 7xy³ and -8x⁵y + 2x³y⁴ + xy³ is 6, while the degree of their difference is 7.
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Description
Test your knowledge on adding and subtracting polynomials with this quiz. Explore various polynomial expressions and profit calculations using polynomial functions. This quiz challenges you to apply your understanding of polynomial operations in real-world scenarios.
