Synthetic Division with Missing Coefficient

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•
Mathematics
•
12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is synthetic division?
Back
Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and is particularly useful when the divisor is a first-degree polynomial.
Tags
CCSS.HSA.APR.D.6
2.
FLASHCARD QUESTION
Front
What is the purpose of finding the value of h in synthetic division problems?
Back
The value of h is determined to ensure that the polynomial division results in a specific quotient and remainder, allowing for the equation to hold true for values of x not equal to the root of the divisor.
Tags
CCSS.HSA.APR.D.6
3.
FLASHCARD QUESTION
Front
How do you set up synthetic division for a polynomial with a missing coefficient?
Back
List the coefficients of the polynomial in descending order of degree, inserting zeros for any missing coefficients. Then, use the synthetic division process with the root of the divisor.
Tags
CCSS.HSA.APR.D.6
4.
FLASHCARD QUESTION
Front
What is the remainder theorem in relation to synthetic division?
Back
The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c). This is useful for finding specific values of polynomials.
Tags
CCSS.HSA.APR.B.2
5.
FLASHCARD QUESTION
Front
Back
Set the coefficients of the corresponding terms equal to each other. For this equation, h must equal 4 to satisfy the equality.
Tags
CCSS.HSA.APR.D.6
6.
FLASHCARD QUESTION
Front
What is the significance of the divisor in synthetic division?
Back
The divisor determines the value of x for which the polynomial is evaluated. It also influences the coefficients of the resulting polynomial after division.
Tags
CCSS.HSA.APR.D.6
7.
FLASHCARD QUESTION
Front
Back
By equating the coefficients of the polynomial on both sides, you find that h must equal 2.
Tags
CCSS.HSA.APR.D.6
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