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Any. They can be integers, rational numbers (the same thing if you multiply out by their LCM), real numbers or even complex numbers.
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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.
What are the rules in addition of polynomials?
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.
Can polynomials have radicals?
no only the coefficients can. like rad 5 but not x or y
Rules in adding polynomials?
To add polynomials , simply combine similar terms. Combine similar terms get the sum of the numerical coefficients and affix the same literal coefficient .
What is the definition of cofficient of polynomial?
The coefficients of polynomials are the numbers in front of the variable expressions. Ex: In the polynomial: 3x^5 + 12x^2 - 45x + 134 the numerical coefficients are: 3,12,& -45
what is irreducible?
An irreducible equation is an irreducible polynomial which is equal to zero. A polynomial is irreducible over a particular type of number if it cannot be factorised into the products of two or more lower degree polynomials with coefficients of that type of number. For example, the equation x2 + 1 =0 is irreducible over the real numbers; there are no lower order polynomials, containing only real coefficients, which could be multiplied together to give this equation.
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 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 irreducible equation?
An irreducible equation is an irreducible polynomial which is equal to zero. A polynomial is irreducible over a particular type of number if it cannot be factorised into the products of two or more lower degree polynomials with coefficients of that type of number. For example, the equation x2 + 1 =0 is irreducible over the real numbers; there are no lower order polynomials, containing only real coefficients, which could be multiplied together to give this equation.
What are the 5 properties of polynomials?
A sum of polynomials is a polynomial.A product of polynomials is a polynomial.A composition of two polynomials is a polynomial, which is obtained by substituting a variable of the first polynomial by the second polynomial.The derivative of the polynomial anxn + an-1xn-1 + ... + a2x2 + a1x + a0 is the polynomial nanxn-1 + (n-1)an-1xn-2 + ... + 2a2x + a1. If the set of the coefficients does not contain the integers (for example if the coefficients are integers modulo some prime number p), then kak should be interpreted as the sum of ak with itself, k times. For example, over the integers modulo p, the derivative of the polynomial xp+1 is the polynomial 0.If the division by integers is allowed in the set of coefficients, a primitive or antiderivative of the polynomial anxn + an-1xn-1 + ... + a2x2 + a1x + a0 is anxn+1/(n+1) + an-1xn/n + ... + a2x3/3 + a1x2/2 + a0x +c, where c is an arbitrary constant. Thus x2+1 is a polynomial with integer coefficients whose primitives are not polynomials over the integers. If this polynomial is viewed as a polynomial over the integers modulo 3 it has no primitive at all.
Can the sum of two polynomials with x as the variable both starting as degree 4 simplify to be of degree 3?
Yes. If and only if the coefficients of x4 are of the same magnitude and opposite sign.
Why do we use polynomials?
To find the curve of a pizza.
