What is the remainder when the given polynomial P x is divided by X?

Answer: If a polynomial p(x) is divided by x-a, then it’s remainder is p(a). Step-by-step explanation: Remainder theorem: According to the remainder theorem, if a polynomial P(x) is divided by the polynomial (x-c), then the remainder is defined as P(c).

When a polynomial P x is divided by a linear polynomial then the remainder is?

ACCORDING TO THE REMAINDER THEOREM, IF ANY POLYNOMIAL p(x) IS DIVIDED A LINEAR DIVISOR (x-a), THEN THE REMAINDER WOULD BE p(a).

What is the remainder when the polynomial is divided by?

If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x) . Synthetic division is a simpler process for dividing a polynomial by a binomial.

What is the remainder when a polynomial P x is divided by XC is it equal to P C )?

Suppose p is a polynomial of degree at least 1 and c is a real number. When p(x) is divided by x−c the remainder is p(c).

What is the remainder when P x?

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 remainder when x 3 1 is divided by x2 x 1?

zero
Summary: The remainder when (x3 + 1) is divided by (x2 – x + 1) is zero.

What is the remainder if a polynomial is divided by (x+2)(x-1)?

A quadratic polynomial when divided by (x+2) leaves a remainder 1, and when divided by (x−1), leaves a remainder 4. What will be the remainder if it is divided by (x+2)(x−1)? Let the quadratic polynomial be denoted as P(x). The polynomial when divided by x+2 gives a remainder of 1. So, from remainder theorom, P(−2)=1.

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 degree of remainder of polynomial P3 and P5?

From remainder theorem of polynomial, p(3)=10 and P(5)=6. If the polynomial is divided by (x−3)(x−5), then the remainder must be of the form ax+b (Since, degree of remainder is less than that of the divisor).

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.