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How do you Explain how your understanding the details of polynomials can help you work through and graph a function. You may include details such as the degree leading coefficient the rational roots f?
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What are the Basic concepts of rational function?
Thee basic concept is that an rational function is one polynomial divided by another polynomial. The coefficients of these polynomials need not be rational numbers.
What is the difference between rational and polynomials?
A polynomial function is simply a function that is made of one or more mononomials. For example 4x^2+3x-5 A rational function is when a polynomial function is divided by another polynomial function.
What is the meaning of rational algebraic expression?
A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.
Can all cubic polynomials be factored into polynomials of degree 1 or 2?
Not into rational factors.
What is expressable as a ratio of two integers or polynomials?
A rational number
What are the Basic concepts of rational function?
Thee basic concept is that an rational function is one polynomial divided by another polynomial. The coefficients of these polynomials need not be rational numbers.
What is a factor that is not the product of polynomials having integer coefficients?
(2/3)x - 6 has a rational coefficient. (sq root 2)x + 4 has an irrational coefficient.
What is the difference between rational and polynomials?
A polynomial function is simply a function that is made of one or more mononomials. For example 4x^2+3x-5 A rational function is when a polynomial function is divided by another polynomial function.
What is the meaning of rational algebraic expression?
A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.
Can all cubic polynomials be factored into polynomials of degree 1 or 2?
Not into rational factors.
What is the formula of rational function?
f(x) = P(x)/Q(x) where P(x) and P(x) are polynomials and P(x) is not zero.
What is expressable as a ratio of two integers or polynomials?
A rational number
What are algebraic fractions whose numerator and denominator are polynomials?
A rational fraction.
What is an expression which contains polynomials in both the numerator and denominator?
rational expression
An expression which contains polynomials in both the numerator and denominator?
rational expression
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
What is the rational root theroem?
In algebra, the rational root theorem (or rational root test, rational zero theorem or rational zero test) states a constraint on rational solutions (or roots) of a polynomialequationwith integer coefficients.If a0 and an are nonzero, then each rational solution x, when written as a fraction x = p/q in lowest terms (i.e., the greatest common divisor of p and q is 1), satisfiesp is an integer factor of the constant term a0, andq is an integer factor of the leading coefficient an.The rational root theorem is a special case (for a single linear factor) of Gauss's lemmaon the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient an = 1.
