Writing Polynomial Functions

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•
Mathematics
•
10th - 11th 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 n is a non-negative integer.
2.
FLASHCARD QUESTION
Front
What are the zeros of a polynomial function?
Back
The zeros (or roots) of a polynomial function are the values of x for which the function equals zero. They can be found by factoring the polynomial or using the quadratic formula.
3.
FLASHCARD QUESTION
Front
How do you find the zeros of the function y=(x + 2)(x - 3)(3x - 5)?
Back
Set the function equal to zero: (x + 2)(x - 3)(3x - 5) = 0. The zeros are x = -2, x = 3, and x = 5/3.
4.
FLASHCARD QUESTION
Front
What is the relationship between the roots and the factors of a polynomial?
Back
Each root of a polynomial corresponds to a factor of the polynomial. If r is a root, then (x - r) is a factor.
5.
FLASHCARD QUESTION
Front
How do you write a polynomial given its roots?
Back
To write a polynomial from its roots, use the factored form: f(x) = a(x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the roots and a is a non-zero constant.
6.
FLASHCARD QUESTION
Front
What is multiplicity in polynomial functions?
Back
Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross the x-axis.
7.
FLASHCARD QUESTION
Front
Given the roots 1, -4, and 1/2, how do you write the polynomial?
Back
The polynomial can be written as f(x) = a(x - 1)(x + 4)(x - 1/2). If a = 2, then f(x) = 2(x - 1)(x + 4)(x - 1/2).
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