Table of Contents
- 1 When the polynomial in P x is divided by X a then remainder equals P A?
- 2 What is the relation between the remainder and the value of the polynomial at x r when the polynomial P x is divided by a binomial of the form x r?
- 3 What is K in a polynomial?
- 4 What does K mean in polynomials?
- 5 What is the remainder of the remainder theorem?
- 6 What is the difference between factor theorem and polynomial remainder?
When the polynomial in P x is divided by X a then remainder equals P A?
The polynomial remainder theorem says that for a polynomial p(x) and a number a, the remainder on division by (x-a) is p(a).
What is the relation between the remainder and the value of the polynomial at x r when the polynomial P x is divided by a binomial of the form x r?
The remainder theorem simply states that if a polynomial f(x) is divided by a linear expression x-r, the value of f(r) is equal to the remainder.
When a polynomial function is divided by xc the remainder is?
When a polynomial is divided by x−c, the remainder is either 0 or has degree less than the degree of x−c. Since x−c is degree 1, the degree of the remainder must be 0, which means the remainder is a constant.
What is K in a polynomial?
k is a zero of f(x) if and only if (x−k) is a factor of f(x) . Each rational zero of a polynomial function with integer coefficients will be equal to a factor of the constant term divided by a factor of the leading coefficient.
What does K mean in polynomials?
The number of positive real zeroes in a polynomial function P(x) is the same or less than by an even number as the number of changes in the sign of the coefficients. So, if there are “K” sign changes, the number of roots will be “k” or “(k – a)”, where “a” is some even number.
How do you find the remainder of a polynomial?
If p (x) is divided by the linear polynomial x – a, then the remainder is p (a). This is the remainder theorem. It helps us to find the remainder without actual division.
What is the remainder of the remainder theorem?
Remainder Theorem Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P (x) by a factor (x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
What is the difference between factor theorem and polynomial remainder?
Here go through a long polynomial division, which results in some polynomial q (x) (the variable “q” stands for “the quotient polynomial”) and a polynomial remainder is r (x). It can be expressed as: Factor Theorem is generally applied to factoring and finding the roots of polynomial equations.
How do you find the remainder of a long division?
Like in this example using Polynomial Long Division: After dividing we get the answer 2x+1, but there is a remainder of 2. But you need to know one more thing: Say we divide by a polynomial of degree 1 (such as “x−3”) the remainder will have degree 0 (in other words a constant, like “4”). We will use that idea in the “Remainder Theorem”: