How do you verify a Remainder Theorem?

Verification: Given, the divisor is (x + 1), i.e. it is a factor of the given polynomial p(x). Remainder = Value of p(x) at x = -1. Hence proved the remainder theorem.

What is Remainder Theorem class 9th?

The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial \[\left( x-a \right)\] then the remainder of that division will be equal to f(a). 7 divided by 2 equals 3 with remainder 1, where 7 is dividend, 2 is divisor, 3 is quotient and 1 is remainder.

What is P C in Remainder Theorem?

Hence, p(c)=(c−c)q(c)=0, so c is a zero of p. Conversely, if c is a zero of p, then p(c)=0. In this case, The Remainder Theorem tells us the remainder when p(x) is divided by (x−c), namely p(c), is 0, which means (x−c) is a factor of p.

What is the remainder when P x is divided by XP where P x x 3 PX 2 6x P?

Answer: The required remainder is 5p.

What is the remainder when the polynomial P x x 3 2x 2 3x K is divided by x 1?

2
Find the remainder when the polynomial x3 – 2×2 + x+1 is divided by x – 1. Substitute the value of x into the polynomial. Therefore, the remainder is 2.

What is P C in remainder theorem?

How do you find C in remainder theorem?

Finding the Remainder using the Remainder Theorem The value of “c” is obtained when the linear factor is expressed in the form x – c. Since the divisor is x + 2, we have x – \left( { – 2} \right) therefore c = – \,2.

What happen when XA is a factor of p x?

Thus, x-a is a factor of p(x) when the remainder is zero. If the (x-a) is a factor of polynomial p(x), then the remainder must be zero. So, we can say that x-a exactly divides p(x). Thus p(x) =0.

How to find the remainder of a polynomial function using remainder theorem?

When a polynomial function f (x) is divided by the linear x-c, then the remainder of polynomial function is always equal to f (c). We know that Dividend = (Divisor x Quotient ) + Remainder r (x) is remainder. Question: Solve (x^4 + 7x^3 + 5x^2 – 4x + 15) \% (x + 2) using remainder theorem?

How do you find the value of K using the remainder theorem?

Given that f ( x) = 2 x 3 + x 2 + k x + 5 divided by 2 x − 3 gives a remainder of 9 1 2, use the remainder theorem to determine the value of k. Therefore k = − 3 and f ( x) = 2 x 3 + x 2 − 3 x + 5.

What is the remainder when divided by T – 1?

By the Remainder Theorem, 2 is the remainder when is divided by t – 1.

What is the reversal form of the remainder theorem?

It is the reversal form of the remainder theorem. Problems are solved based on the application of synthetic division and then to check for a zero remainder. When p (x) = 0 then y-x is a factor of the polynomial Or if we consider the other way, then When y-x is a factor of the polynomial then p (x) =0