Questions and Answers
If -1 is a root of f(x), which of the following must be true?
What dividend is represented by the synthetic division below?
2x^3 + 10x^2 + x + 5
Use synthetic division to solve (3x^4 + 6x^3 + 2x^2 + 9x + 10). What is the quotient?
3x^3 + 2x + 5
What are all the roots of the function if one factor of f(x) = 5x^3 + 5x^2 - 170x + 280 is (x + 7)?
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Use synthetic division to solve (x^3 + 1) ÷ (x - 1). What is the quotient?
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What are all the roots of the function if one factor of f(x) = 4x^3 - 4x^2 - 16x + 16 is (x - 2)?
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Use synthetic division to solve (2x^3 + 4x - 35x + 15) divided by (x - 3). What is the quotient?
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Use synthetic division to solve (4x^3 - 3x^2 + 5x + 6) divided by (x + 6). What is the quotient?
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What divisor is represented by the synthetic division below?
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If f(1) = 0, what are all the roots of the function f(x) = x^3 + 3x^2 - x - 3?
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Study Notes
Synthetic Division and the Remainder Theorem
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If -1 is a root of f(x), then (x + 1) is a factor of f(x).
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The dividend represented by synthetic division for the polynomial is 2x^3 + 10x^2 + x + 5.
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Using synthetic division on (3x^4 + 6x^3 + 2x^2 + 9x + 10) results in a quotient of (3x^3 + 2x + 5).
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For the polynomial (f(x) = 5x^3 + 5x^2 - 170x + 280) with a known factor (x + 7), the roots found using the Remainder Theorem are x = -7, x = 2, and x = 4.
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Synthetic division of ((x^3 + 1)) by ((x - 1)) yields a quotient of (x^2 + x + 1 + \frac{2}{x - 1}).
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For (f(x) = 4x^3 - 4x^2 - 16x + 16) with a factor (x - 2), the roots are x = -2, x = 1, and x = 2.
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Dividing (2x^3 + 4x - 35x + 15) by ((x - 3)) through synthetic division produces a quotient of (3x^2 + 10x - 5).
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The quotient obtained from synthetic division of (4x^3 - 3x^2 + 5x + 6) by ((x + 6)) is (4x^2 - 27x + 167 - \frac{996}{x + 6}).
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The divisor shown in a synthetic division example corresponds to (x + 5).
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Given that (f(1) = 0), the roots found for (f(x) = x^3 + 3x^2 - x - 3) are x = -3, x = -1, and x = 1.
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Description
Test your understanding of synthetic division and the Remainder Theorem with this quiz. You'll explore concepts such as factors, dividends, and how to find quotients through synthetic division. Perfect for mathematics students looking to reinforce their knowledge in polynomial functions.
