What is Remainder Theorem with example?
So basically, x -a is the divisor of P(x) if and only if P(a) = 0. 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.
Why does 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.
What is remainder theorem explain?
: 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)
How do you calculate the 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 remainder and factor theorem?
Factor Theorem is a special case of Remainder Theorem. Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x – a) then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x – a) is a factor of polynomial ƒ(x).
What is remainder theorem proof?
Proof of Remainder Theorem You know that Dividend = (Divisor × Quotient) + Remainder. If r(x) is the constant then, p(x) = (x-c)·q(x) + r. Let us put x=c. p(c) = (c-c)·q(c) + r. p(c) = (0)·q(c) + r.
What is the 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 does the remainder theorem work?
The remainder theorem states that f (a) is the remainder when the polynomial f (x) is divided by x – a. Thus, given a polynomial, f (x), which is to be divided by a linear binomial of the form x – a, the remainder of the division is given by f (a).
What is the quotient in the remainder theorem?
This theorem is sometimes called the division algorithm. When you divide one positive integer, called the divisor, into another, called the dividend, you get a quotient and a remainder which may be 0. The quotient is the largest number whose product with the divisor is less than or equal to the dividend.
What is synthetic division and remainder theorem?
I introduce Synthetic Division and the Remainder Theorem. Synthetic division is a short cut to long division when you are dividing by a binomial in the form of (x-c). The Remainder Theorm is how you can use Synthetic Division to aid in evaluating polynomials at particular x values.
What is the remainder of a polynomial?
The Remainder Theorem tells us that if one divides a polynomial by (x-r) then the remainder is the value of that polynomial for x = r. So the remainder when is divided by (x+1), or (x-(-1)), is the same as the value of when x = -1.