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Use Rational Root Theorem to find the Zeros of the Polynomial
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
FREE Resource
Student preview
15 questions
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1.
FLASHCARD QUESTION
Front
What is the Rational Root Theorem?
Back
The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of p/q, is such that p is a factor of the constant term and q is a factor of the leading coefficient.
Tags
CCSS.HSA.APR.B.2
2.
FLASHCARD QUESTION
Front
How do you determine if a polynomial has a rational root?
Back
To determine if a polynomial has a rational root, use the Rational Root Theorem to list all possible rational roots, then test these roots using synthetic division or substitution.
Tags
CCSS.HSA.APR.B.2
3.
FLASHCARD QUESTION
Front
What is synthetic division?
Back
Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is quicker and requires less writing.
Tags
CCSS.HSA.APR.D.6
4.
FLASHCARD QUESTION
Front
What does it mean if the remainder is zero in synthetic division?
Back
If the remainder is zero when using synthetic division, it means that the divisor (x - c) is a factor of the polynomial, and c is a root of the polynomial.
Tags
CCSS.HSA.APR.D.6
5.
FLASHCARD QUESTION
Front
Given f(x) = 2x^3 - 19x^2 + 38x + 24, if (x - 4) is a factor, what is one zero of the function?
Back
One zero of the function is x = 4.
Tags
CCSS.HSA.APR.B.2
6.
FLASHCARD QUESTION
Front
How can you find all zeros of a polynomial?
Back
To find all zeros of a polynomial, first identify any rational roots using the Rational Root Theorem, then use synthetic division to factor the polynomial, and finally solve the resulting factors.
7.
FLASHCARD QUESTION
Front
What are the possible rational zeros of a polynomial?
Back
The possible rational zeros of a polynomial can be found by taking the factors of the constant term and dividing them by the factors of the leading coefficient.
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