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A comprehensive solution to various polynomial problems, including finding the greatest common factor, completely factoring polynomials, performing polynomial division using synthetic division, and solving polynomial equations. The solutions cover a wide range of topics, such as factoring, remainder theorem, and substitution methods. Structured in a question-and-answer format, making it a valuable resource for students studying polynomials. The solutions are presented in a clear and concise manner, making it easy for readers to understand and apply the concepts. Overall, this document is a valuable tool for students and educators interested in mastering polynomial operations and problem-solving.
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What is the greatest common factor of the terms in the polynomial 3x³ - 3x² - 18x? << answer >>3x What is the greatest common factor of the terms in the polynomial 8x⁴ - 4x³ - 18x²? << answer >>2x² What is the greatest common factor of the terms in the polynomial 12x⁴ + 27x³ + 6x²? << answer >>3x² Which is the completely factored form of 4x³ + 10x² - 6x? << answer
2x(x + 3)(2x - 1) Which is the completely factored form of 12x³ - 60x² + 4x - 20? << answer >>4(3x² + 1)(x - 5) What is the greatest common factor of the terms in the polynomial 4x⁴ - 32x³ - 60x²? << answer >>4x²
The quotient of (x⁴ + 5x³ - 3x - 15) and a polynomial is (x³ - 3). What is the polynomial? << answer >>x + 5 What is the quotient (125 - 8x³) ÷ (25 + 10x + 4x²)? << answer >>-2x + 5 What remainder is represented by the synthetic division below? -5|2 10 1 5
.. |_-10 0- .. .2 .0 .1 0 << answer >> Use synthetic division to solve (x³ + 1) ÷ (x - 1). What is the quotient? << answer >>x³ - x² + x One root of f(x) = x³ - 4x² - 20x + 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem. << answer >>(x - 2)(x + 4) (x - 6) The volume of a rectangular prism is 2x³ + 9x² - 8x - 36 with height x +
2x² + 5x - 18 Use synthetic division to solve (2x³ + 4x² - 35x + 15) / (x - 3). What is the quotient? << answer >>2x² + 10x -
If (x + 8) is a factor of f(x), which of the following must be true? << answer >>f(-8) = 0 What dividend is represented by the synthetic division below? -5| 2 10 1 5
.. |_ -10 0- ... 2 .0 .1 0 << answer >>2x³ + 10x² + x + 5 The area of a rectangle is 5x³ + 19x² + 6x - 18 with length x + 3. Using synthetic division, what is the width of the rectangle? << answer >>5x²