What is the factor theorem on polynomial long division?
What is the factor theorem on polynomial long division?
According to the Factor Theorem: If we divide a polynomial f(x) by (x – c), and (x – c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x – c) must be a factor.
How is the remainder theorem related to long division?
That is, when you divide by “x – a”, your remainder will just be some number. 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.
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 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 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 formula of factor theorem?
Answer: The Factor Theorem explain us that if the remainder f(r) = R = 0, then (x − r) happens to be a factor of f(x). The Factor Theorem is quite important because of its usefulness to find roots of polynomial equations.
How are remainder and factor theorems used to divide polynomials?
Dividing Polynomials; Remainder and Factor Theorems 2.4 Dividing polynomials; Remainder and Factor Theorems Use long division to divide polynomials. Use synthetic division to divide polynomials. Evaluate a polynomials using the Remainder Theorem. Use the Factor Theorem to solve a polynomial equation.
Which is an example of a polynomial long division?
Like in this example using Polynomial Long Division: After dividing we get the answer 2x+1, but there is a remainder of 2. But you need to know one more thing: Say we divide by a polynomial of degree 1 (such as “x−3”) the remainder will have degree 0 (in other words a constant, like “4”).
How is remainder related to divisor and dividend?
Here the remainder is zero thus we can say 5 is a factor of 25 or 25 is a multiple of 5. Thus reminder gives us a link between dividend and the divisor. We can divide a polynomial by another polynomial and can express in the same way.
Which is the correct formula for remainder factor?
Through trial and error, we obtain f ( 1) = 6 − 23 − 6 + 8 = − 15 f ( 2) = 48 − 92 − 12 + 8 = − 48 f ( 4) = 384 − 368 − 24 + 8 = 0 f ( 1 2) = 3 4 − 5 3 4 − 3 + 8 = 0 f ( − 1 2) = − 3 4 − 5 3 4 + 3 + 8 = 4 1 2 f ( − 2 3) = − 1 7 9 + 10 2 9 + 4 + 8 = 0. + 4+8 = 0.