5.2 Writing Polynomial Equations Given Roots
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
+3
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is a polynomial?
Back
A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and multiplied by coefficients. For example, 2x^2 + 3x + 1 is a polynomial.
2.
FLASHCARD QUESTION
Front
What are the roots of a polynomial?
Back
The roots of a polynomial are the values of the variable that make the polynomial equal to zero. They are also known as zeros or solutions of the polynomial.
3.
FLASHCARD QUESTION
Front
How do you find a polynomial given its roots?
Back
To find a polynomial given its roots, you can use the factored form: if r1, r2, ..., rn are the roots, the polynomial can be expressed as (x - r1)(x - r2)...(x - rn).
Tags
CCSS.HSA.APR.B.3
4.
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 the polynomial 3x^4 + 2x^3 - x + 5, the degree is 4.
5.
FLASHCARD QUESTION
Front
What is the standard form of a polynomial?
Back
The standard form of a polynomial is when it is written in descending order of the degree of its terms. For example, 2x^3 + 3x^2 - x + 4 is in standard form.
6.
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 factors. For example, x^2 - 5 can be factored as (x - √5)(x + √5).
Tags
CCSS.HSA.APR.C.4
7.
FLASHCARD QUESTION
Front
What is the relationship between roots and factors of a polynomial?
Back
If r is a root of a polynomial, then (x - r) is a factor of that polynomial. This means that if you know the roots, you can write the polynomial in factored form.
Tags
CCSS.HSA.APR.B.2
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