What is the remainder when x3 x 1 is divided by 2x 1?

What is the remainder when x3 x 1 is divided by 2x 1?

5/8
The remainder when x3 – x + 1 is divided by 2x – 1, by using remainder theorem is 5/8.

When x 3 3x 2 3x 1 is divided by x 1 What is the remainder?

Hence by the remainder theorem, 0 is the remainder when x3 + 3×2 + 3x + 1 is divided by x + 1. We can also say that x + 1 is a factor of x3 + 3×2 + 3x + 1. (ii) The root of x – (1/2) = 0 is 1/2. Hence by the remainder theorem, 27 / 8 is the remainder when x3 + 3×2 + 3x + 1 is divided by x.

How do you find the value of x in the remainder theorem?

Important Notes

1. When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k)
2. The remainder theorem formula is: p(x) = (x-c)·q(x) + r(x).
3. The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

What is the remainder when x3 1 is divided by x 1?

0
So, when f(x) = x3 + 1 is divided by x + 1, the remainder obtained is zero. Therefore, the remainder is 0.

What is the value of K if X 1 is a factor of 4×3 3×2 4x K?

Textbook solution k=−3.

Is 7 3x a factor of 3×3 7x?

Check whether 7 + 3x is a factor of 3×3 + 7x When a polynomial p(x) is divided by x – a then by factor theorem if p(a) = 0, we can say that x – a is a factor of p(x). For 7 + 3x to be a factor, it is very important for the remainder to be equal to 0. The root of 7 + 3x = 0 is -7 / 3.

When 15sqrt 15 is Divided by 3sqrt 3 What is the quotient?

In this question, we have to find the quotient on dividing the $ 3\sqrt 3 $ with $ 15\sqrt {15} $ . This can also be solved by another method . So, the correct answer is “ $ 5\sqrt 5 $ ”.

When a polynomial P x is divided by XA?

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).

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 theorem of Division?

The remainder theorem is stated as follows: When a polynomial a (x) is divided by a linear polynomial b (x) whose zero is x = k, the remainder is given by r = a (k). The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the division algorithm.

When a polynomial is divided by a linear divisor?

In general, whenever a polynomial is divided by a linear divisor and the remainder is 0, the linear divisor must be a factor of the polynomial. Find the remainder polynomial and the quotient when a (x) is divided by b (x) using the remainder theorem.

What is an example of remainders in math?

Example 8: Let R 1 and R 2 are the remainders when the polynomials x 3 + 2x 2 –5ax–7 and x 3 + ax 2 – 12x + 6 are divided by x + 1 and x – 2 respectively. If 2R 1 + R 2 = 6, find the value of a.