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Questions and Answers
What is the result of simplifying the expression $(-4m²n)⁴ \div 6m^{-10}$?
What is the result of simplifying the expression $(-4m²n)⁴ \div 6m^{-10}$?
The result is $\frac{256m^{8}n^{4}}{6}$ or $\frac{128m^{8}n^{4}}{3}$ in standard form.
Combine and simplify the expression $(8a² − 6 − 8a) + (1 − 6a − 7a²)$ in standard form.
Combine and simplify the expression $(8a² − 6 − 8a) + (1 − 6a − 7a²)$ in standard form.
The simplified expression is $-a² - 14a - 5$.
What does the expression $(y+4)³ - 2y(y−1)$ simplify to?
What does the expression $(y+4)³ - 2y(y−1)$ simplify to?
The simplified expression is $y³ + 10y² + 50y + 64$.
Factor the polynomial $3n² − 147$ completely.
Factor the polynomial $3n² − 147$ completely.
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Expand the expression $(3k − 6)(k² − k + 7)$ and write it in standard form.
Expand the expression $(3k − 6)(k² − k + 7)$ and write it in standard form.
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Study Notes
Polynomial Functions Study Guide
- Simplify expressions: Examples of simplifying polynomial expressions are shown.
- Polynomial operations: Combine and simplify polynomials according to the rules of polynomial arithmetic.
- Classifying polynomials: Identify expressions as polynomials and classify them by degree.
- Factoring polynomials: Factor out the common factors to simply an expression.
- Sum of Cubes: The formula for the sum of cubes is a³+b³=(a+b)(a²-ab+b²).
- Differences of Cubes: The formula for the differences of cubes is a³-b³=(a-b)(a²+ab+b²).
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Description
This study guide covers key concepts in polynomial functions, including simplifying expressions, performing polynomial operations, and classifying polynomials by degree. It also explains how to factor polynomials and provides formulas for the sum and difference of cubes to enhance your understanding.
