Polynomial Function (non-calc)

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•
Mathematics
•
9th - 10th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a polynomial function?
Back
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: $$f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$$ where \(a_n, a_{n-1}, ..., a_0\) are constants and \(n\) is a non-negative integer.
2.
FLASHCARD QUESTION
Front
What are the zeros of a polynomial function?
Back
The zeros of a polynomial function are the values of \(x\) for which the function equals zero. They are also known as the roots of the polynomial.
3.
FLASHCARD QUESTION
Front
How do you find the zeros of a polynomial function?
Back
To find the zeros of a polynomial function, set the function equal to zero and solve for \(x\). This may involve factoring, using the quadratic formula, or other algebraic methods.
4.
FLASHCARD QUESTION
Front
What is the factored form of a polynomial?
Back
The factored form of a polynomial expresses it as a product of its linear factors. For example, if the zeros of a polynomial are \(x = r_1, r_2, ..., r_n\), the factored form is: $$f(x) = a(x - r_1)(x - r_2)...(x - r_n)$$ where \(a\) is a leading coefficient.
5.
FLASHCARD QUESTION
Front
What is the degree of a polynomial?
Back
The degree of a polynomial is the highest power of the variable in the polynomial. For example, in \(f(x) = 4x^3 + 2x^2 - x + 7\), the degree is 3.
6.
FLASHCARD QUESTION
Front
What is the leading coefficient of a polynomial?
Back
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in \(f(x) = 3x^4 + 2x^3 - x + 5\), the leading coefficient is 3.
7.
FLASHCARD QUESTION
Front
What is multiplicity in relation to polynomial zeros?
Back
Multiplicity refers to the number of times a particular zero appears in a polynomial. For example, if \(x = 2\) is a zero of the polynomial \(f(x) = (x - 2)^3(x + 1)\), then it has a multiplicity of 3.
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