Questions and Answers
What is the condition for cx - d to be a factor of p(x) according to the Factor Theorem?
What can be concluded if p(d/c) = 0?
What is the general form of a polynomial p(x) that has a factor cx - d?
What is the relationship between the remainder and the Factor Theorem?
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What is a useful application of the Factor Theorem?
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What can be concluded if p(x) has a root d/c?
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If p(x) is a polynomial and cx - d is a factor of p(x), what can be concluded about p(d/c)?
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If p(x) is a polynomial and p(d/c) = 0, what can be concluded about cx - d?
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What is the polynomial Q(x) in the expression p(x) = (cx - d)Q(x)?
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Why is the Factor Theorem particularly useful for factorizing cubic polynomials?
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What is the relationship between the roots of a polynomial p(x) and its factors?
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What is a special case of the Remainder Theorem?
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If $p(x) = x^3 + 2x^2 - 7x - 12$ and $p(-2) = 0$, what can be concluded about the factorization of $p(x)$?
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If $p(x) = x^2 - 4x - 3$ and $cx - d$ is a factor of $p(x)$, what can be concluded about the value of $c$ and $d$?
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If $p(x) = x^4 - 2x^3 - 3x^2 + 6x + 1$ and $p(1) = 0$, what can be concluded about the factorization of $p(x)$?
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If $p(x) = 2x^3 + 5x^2 - 3x - 1$ and $cx - d$ is a factor of $p(x)$, what is the degree of the quotient polynomial $Q(x)$?
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If $p(x) = x^3 - 2x^2 - 5x + 6$ and $p(-3) = 0$, what can be concluded about the value of $p(-3/2)$?
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If $p(x) = x^4 - 4x^3 + 7x^2 - 12x + 9$ and $cx - d$ is a factor of $p(x)$, what can be concluded about the value of $c$ and $d$?
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