What is a polynomial function?
MAT 171 Unit 4 Review 3

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Mathematics
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10th - 12th Grade
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Hard
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1.
FLASHCARD QUESTION
Front
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 does the Complex Conjugate Root Theorem state?
Back
The Complex Conjugate Root Theorem states that if a polynomial has real coefficients and a complex number a + bi is a root, then its complex conjugate a - bi is also a root.
3.
FLASHCARD QUESTION
Front
If a + bi is a root of a polynomial, what is the other root?
Back
The other root is a - bi.
4.
FLASHCARD QUESTION
Front
How do you find a polynomial function with given zeros?
Back
To find a polynomial function with given zeros, use the fact that if r is a root, then (x - r) is a factor. Multiply the factors corresponding to all the roots to get the polynomial.
5.
FLASHCARD QUESTION
Front
What is the least degree of a polynomial?
Back
The least degree of a polynomial is the smallest exponent of the variable in the polynomial when it is expressed in standard form.
6.
FLASHCARD QUESTION
Front
What are integral coefficients in a polynomial?
Back
Integral coefficients are the numerical factors in a polynomial that are whole numbers (positive, negative, or zero).
7.
FLASHCARD QUESTION
Front
Write a polynomial function of least degree with integral coefficients that has the zeros -1, 5, and 2i.
Back
The polynomial is (x + 1)(x - 5)(x - 2i)(x + 2i) = (x + 1)(x - 5)(x^2 + 4) = x^4 - 4x^3 - 19x^2 + 20x + 20.
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