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 factor theorem with examples?

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 remainder theorem and factor 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 the formula of remainder?

In the abstract, the classic remainder formula is: Dividend/Divisor = Quotient + Remainder/Divisor. If we multiply through by the Divisor, we get another helpful variant of the remainder formula: Dividend = Quotient*Divisor + Remainder.

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.

What is the difference between remainder 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 factor theorem formula?

⟹ f(x) = (x – c) q(x) Hence, (x – c) is a factor of the polynomial f (x). Hence, the Factor Theorem is a special case of Remainder Theorem, which states that a polynomial f (x) has a factor x – a, if and only if, a is a root i.e., f (a) = 0.

Is factor theorem same as remainder theorem?

Is factor theorem and remainder theorem are same?

What is the remainder theorem formula?

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.

Is the factor theorem related to the remainder theorem?

The Factor theorem is a unique case consideration of the polynomial remainder theorem. Thus the factor theorem states that a polynomial has a factor if and only if: The polynomial x – M is a factor of the polynomial f (x) if and only if f (M) = 0. Factor theorem is frequently linked with the remainder theorem, therefore do not confuse both.

Which is a factor of the remainder f ( x )?

The Factor Theorem states: If the remainder f(r) = R = 0, then (x − r) is a factor of f(x). The Factor Theorem is powerful because it can be used to find roots of polynomial equations. Is (x + 1) a factor of f(x) = x 3 + 2x 2 − 5x − 6?

When does the remainder of a polynomial equal h?

If you divide a polynomial f(x) by (x – h), then the remainder is f(h). The theorem states that our remainder equals f(h). Therefore, we do not need to use long division, but just need to evaluate the polynomial when x = h to find the remainder. We should understand why this theorem is true.

How is the factor theorem used in polynomial equations?

The Factor Theorem is powerful because it can be used to find roots of polynomial equations. Is (x + 1) a factor of f(x) = x3 + 2×2 − 5x − 6? In this case we need to test the remainder `r = -1`. Therefore, since `f (-1) = 0`, we conclude that ` (x + 1)` is a factor of `f (x)`. 1. Find the remainder R by long division and by the Remainder Theorem.