Writing Polynomial Functions

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
+2
Standards-aligned
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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 does it mean for a polynomial to be in standard form?
Back
A polynomial is in standard form when it is written as a sum of terms in descending order of the degree of each term, starting from the highest degree to the constant term.
3.
FLASHCARD QUESTION
Front
How do you find the zeros of a polynomial function?
Back
The zeros of a polynomial function are the values of x for which f(x) = 0. They can be found by factoring the polynomial or using the quadratic formula for polynomials of degree 2.
Tags
CCSS.HSF-IF.C.7C
4.
FLASHCARD QUESTION
Front
What is the relationship between the zeros and the factors of a polynomial?
Back
Each zero of a polynomial corresponds to a factor of the form (x - zero). For example, if x = 3 is a zero, then (x - 3) is a factor.
Tags
CCSS.HSF-IF.C.7C
5.
FLASHCARD QUESTION
Front
How do you write a polynomial given its zeros?
Back
To write a polynomial given its zeros, use the factored form: f(x) = a(x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the zeros and a is a non-zero constant.
Tags
CCSS.HSA.APR.B.3
6.
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) = 2x^3 + 3x^2 - x + 5, the degree is 3.
7.
FLASHCARD QUESTION
Front
What is a leading coefficient?
Back
The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 4x^3 + 2x^2 - 5, the leading coefficient is 4.
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