What is the remainder theorem in algebra 2?

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 a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).

What is Remainder Theorem explain?

Definition of remainder theorem



: a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x − a is f(a)

What is the Remainder Theorem example?

The Remainder Theorem then points out the connection between division and multiplication. For instance, since 12 ÷ 3 = 4, then 4 × 3 = 12. If you get a remainder, you do the multiplication and then add the remainder back in. For instance, since 13 ÷ 5 = 2 R 3, then 13 = 5 × 2 + 3.

What is remainder theorem formula?

The remainder theorem formula is: p(x) = (x-c)·q(x) + r(x). The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

How do you solve the remainder theorem?

Video quote: So in the first one notice we've got a 3x cubed minus 2x squared plus X minus 6. That's our f of X that's being divided in this case we're dividing by X minus 4.

Why do we use the remainder theorem?

The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily.

What is remainder theorem for Class 10?

According to the remainder theorem, if is divided by then, the remainder is given by, If is divided by , then the remainder is given by, Hence, a polynomial when divided by leaves a remainder 3 and when divided by leaves a remainder 1. Then if the polynomial is divided by , it leaves a remainder .

What is remainder theorem in Class 9?

Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Proof: Let p(x) be any polynomial with degree greater than or equal to 1.

What is factor theorem with example?

Answer: An example of factor theorem can be the factorization of 6×2 + 17x + 5 by splitting the middle term. In this example, one can find two numbers, ‘p’ and ‘q’ in a way such that, p + q = 17 and pq = 6 x 5 = 30. After that one can get the factors.

What is the remainder if 825 is divided by 7?

6 is the remainder of this division.

What’s a remainder number?

In mathematics, the remainder is the amount “left over” after performing some computation. In arithmetic, the remainder is the integer “left over” after dividing one integer by another to produce an integer quotient (integer division).

What is the remainder when 2 power 35 divided by 5?

Answer. the remainder is three.

What is the remainder of 8 25 is divided by?

Remainder of (8 power 25) divided by 7 is 1.

What is the remainder when 125 divided by 10 31?

By 10^31, then the Remainder is 0. 10^31 has 31 zeroes.

What is the remainder when 235 is divided by 5?

Here, we will be using divisibility by 5 rule. Now, 235 has 5 as its last digit. Which means, 235 is divisible by 5. And, we will get zero as the remainder when the dividend is divisible by the divisor.

What is the remainder of 21 divided by 7?

R D Sharma – Mathematics 9



Solution – On performing divison of 21 by 7, the remainder left will be zero. The quotient will be 3.

What is the remainder of 48 divided by 8?

Subtract 48 from 48 . The result of division of 48÷8 48 ÷ 8 is 6 .

What is the remainder of 24 divided by 6?

Using a calculator, if you typed in 24 divided by 6, you’d get 4. You could also express 24/6 as a mixed fraction: 4 0/6. If you look at the mixed fraction 4 0/6, you’ll see that the numerator is the same as the remainder (0), the denominator is our original divisor (6), and the whole number is our final answer (4).

What is the remainder of 24 divided by 4?

The result of division of 24÷4 24 ÷ 4 is 6 .

What is the 48 split into 6?

Using a calculator, if you typed in 48 divided by 6, you’d get 8.

How do you solve 18 divided by 2?

The answer to 18 divided by 2 is 9 (18 / 2 = 9).

What is the remainder of 48 divided by 4?

Using a calculator, if you typed in 48 divided by 4, you’d get 12. You could also express 48/4 as a mixed fraction: 12 0/4. If you look at the mixed fraction 12 0/4, you’ll see that the numerator is the same as the remainder (0), the denominator is our original divisor (4), and the whole number is our final answer (12) …

How do you write 55 divided by 5?

Using a calculator, if you typed in 55 divided by 5, you’d get 11. You could also express 55/5 as a mixed fraction: 11 0/5.

What is the remainder of 48 divided by 2?

Using a calculator, if you typed in 48 divided by 2, you’d get 24. You could also express 48/2 as a mixed fraction: 24 0/2. If you look at the mixed fraction 24 0/2, you’ll see that the numerator is the same as the remainder (0), the denominator is our original divisor (2), and the whole number is our final answer (24) …