What is the remainder theorem in algebra 2?

What is the remainder theorem in algebra 2? where q(x) is a polynomial with one degree less than the degree of f(x) and f(r) is the remainder. This is called the remainder theorem. If the remainder f(r) = 0, then (x − r) is a factor of f(x).

What is remainder theorem with example? It is applied to factorize polynomials of each degree in an elegant manner. For example: if f(a) = a3-12a2-42 is divided by (a-3) then the quotient will be a2-9a-27 and the remainder is -123. Thus, it satisfies the remainder theorem.

What is the remainder theorem for dummies? The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x – a, the remainder of that division will be equivalent to f(a).

What is remainder theorem Class 9 formula? If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). In particular, if x = a, then eq (ii) becomes p(a) = (a – a) q(a) + r = r, Solution: Zero of x – 1 is 1, so as per remainder theorem remainder in this case will be p(1) .

What is the remainder theorem in algebra 2? – Related Questions

What is the quotient remainder formula?

The dividend divisor quotient remainder formula can be applied if we know either the dividend or remainder or divisor. The formula can be applied accordingly. For dividend, the formula is: Dividend = Divisor × Quotient + Remainder. For divisor, the formula is: Dividend/Divisor = Quotient + Remainder/Divisor.

How does a remainder theorem work?

The remainder theorem is a close cousin of the factor theorem, and says that when you divide by , the remainder you get is . Notice that this fits perfectly well with the factor theorem: if the remainder when you divide by something is zero, what you divided by is a factor!

What is the difference between remainder theorem and factor theorem?

Basically, the remainder theorem links remainder of division by a binomial with the value of a function at a point, while the factor theorem links the factors of a polynomial to its zeros.

How else do you call the quotient when the remainder is zero?

When one term (the “dividend”) is divided by another term (the “divisor”), the result is a “quotient” and a “remainder”. When the remainder is zero, both the quotient and divisor are factors of the dividend.

How do I get a remainder?

Work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that’s left by the divisor of your original problem. The result is your remainder. For example, divide 346 by 7 to arrive at 49.428571.

What is divisor formula?

Divisor Formula

Let us understand the formula of divisor when the remainder is 0, and when it is a non-zero number. If the remainder is 0, then Divisor = Dividend ÷ Quotient. If the remainder is not 0, then Divisor = (Dividend – Remainder)/ Quotient.

How do you find the quotient?

The quotient is the number obtained by dividing one number by another. For example, if we divide the number 6 by 3, the result so obtained is 2, which is the quotient. It is the answer from the division process. The quotient can be an integer or a decimal number.

What is the quotient and remainder?

3.1 Quotients and Remainders

The number of times we have subtracted b is called the quotient (of the division of a by b ) The number that is leftover from a after subtracting b as often as possible is called the remainder (of the division of a by b ).

When a number is divided by 121 what is the remainder is 25?

x divided by 121 yields a reminder of 25. Since 121 is a multiple of 11 (11 x 11), we can assume that when x is divided by 11, it will also yield a reminder of 25. However, 25 can further be divided by 11 to yield a remainder of 3 (11 x 2). For instance, lets take the example of x = 146.

When should we use remainder theorem?

The remainder theorem formula is used to find the remainder when a polynomial p(x) is divided by (ax + b). Using the remainder theorem we can determine whether (ax + b) is a factor of p(x) or not. If the remainder is 0, then (ax + b) is a factor of a polynomial p(x), otherwise, it is not.

What is Factor Theorem and remainder theorem Class 9?

Factor Theorem. Factor Theorem. x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number. This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

What is the use of factor theorem in real life?

Factor theorem is mainly used to factor the polynomials and to find the n roots of the polynomials. Factor theorem is very helpful for analyzing polynomial equations. In real life, factoring can be useful while exchanging money, dividing any quantity into equal pieces, understanding time, and comparing prices.

What is the quotient of 5 0?

The quotient (integer division) of 0/5 equals 0; the remainder (“left over”) is 0. 0 is the dividend, and 5 is the divisor.

What is the quotient of 0 divided by 2?

That means, when we divide $0$ by $-2,$ we will get $0$ as the quotient. We learn that the given statement has a solution. Note: When the divisor is zero, then the value is undefined. The quotient we obtain when a number is divided by zero is infinity.

What is the quotient of 0 10?

The quotient (integer division) of 0/10 equals 0; the remainder (“left over”) is 0. 0 is the dividend, and 10 is the divisor.

What is the remainder when 51 * 27 * 35 * 62 * 75?

∴ The answer is 50.

What is the remainder of 17 divided by 3?

The result of division of 173 is 5 with a remainder of 2 .

What is the greatest remainder when you divide by 3?

The greatest remainder you could have with the divisor 3 is 2, with the divisor 8 is 7, and with the divisor 5 is 4. If the remainder is more than the divisor, another group can be divided into the dividend.

Does 1 count as a divisor?

whose only proper divisor is 1 is called a prime number. Equivalently, a prime number is a positive integer that has exactly two positive factors: 1 and itself.

Is divisor and factor the same?

The divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.