Podcast
Questions and Answers
What is the condition for cx - d to be a factor of p(x) according to the Factor Theorem?
What is the condition for cx - d to be a factor of p(x) according to the Factor Theorem?
- If p(d/c) is a negative number
- If p(d/c) is a positive number
- If p(d/c) is a non-zero constant
- If p(d/c) is zero (correct)
What can be concluded if p(d/c) = 0?
What can be concluded if p(d/c) = 0?
- cx - d is a factor of p(x) (correct)
- p(x) is a quadratic polynomial
- p(x) is a linear polynomial
- cx - d is not a factor of p(x)
What is the general form of a polynomial p(x) that has a factor cx - d?
What is the general form of a polynomial p(x) that has a factor cx - d?
- p(x) = (cx - d) \* Q(x) (correct)
- p(x) = Q(x) / (cx - d)
- p(x) = cx - d + Q(x)
- p(x) = cx - d / Q(x)
What is the relationship between the remainder and the Factor Theorem?
What is the relationship between the remainder and the Factor Theorem?
What is a useful application of the Factor Theorem?
What is a useful application of the Factor Theorem?
What can be concluded if p(x) has a root d/c?
What can be concluded if p(x) has a root d/c?
If p(x) is a polynomial and cx - d is a factor of p(x), what can be concluded about p(d/c)?
If p(x) is a polynomial and cx - d is a factor of p(x), what can be concluded about p(d/c)?
If p(x) is a polynomial and p(d/c) = 0, what can be concluded about cx - d?
If p(x) is a polynomial and p(d/c) = 0, what can be concluded about cx - d?
What is the polynomial Q(x) in the expression p(x) = (cx - d)Q(x)?
What is the polynomial Q(x) in the expression p(x) = (cx - d)Q(x)?
Why is the Factor Theorem particularly useful for factorizing cubic polynomials?
Why is the Factor Theorem particularly useful for factorizing cubic polynomials?
What is the relationship between the roots of a polynomial p(x) and its factors?
What is the relationship between the roots of a polynomial p(x) and its factors?
What is a special case of the Remainder Theorem?
What is a special case of the Remainder Theorem?
If $p(x) = x^3 + 2x^2 - 7x - 12$ and $p(-2) = 0$, what can be concluded about the factorization of $p(x)$?
If $p(x) = x^3 + 2x^2 - 7x - 12$ and $p(-2) = 0$, what can be concluded about the factorization of $p(x)$?
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 $d$?
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 $d$?
If $p(x) = x^4 - 2x^3 - 3x^2 + 6x + 1$ and $p(1) = 0$, what can be concluded about the factorization of $p(x)$?
If $p(x) = x^4 - 2x^3 - 3x^2 + 6x + 1$ and $p(1) = 0$, what can be concluded about the factorization of $p(x)$?
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 $Q(x)$?
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 $Q(x)$?
If $p(x) = x^3 - 2x^2 - 5x + 6$ and $p(-3) = 0$, what can be concluded about the value of $p(-3/2)$?
If $p(x) = x^3 - 2x^2 - 5x + 6$ and $p(-3) = 0$, what can be concluded about the value of $p(-3/2)$?
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 $d$?
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 $d$?
