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What is a remainder theorem?
Why is the remainder theorem used in polynomial division?
What is the difference between factor and remainder theorem?
What is the remainder theorem in Class 9?
The Remainder Theorem. When we divide f (x) by the simple polynomial x−c we get: f (x) = (x−c) q (x) + r (x) x−c is degree 1, so r (x) must have degree 0, so it is just some constant r: f (x) = (x−c) q (x) + r. Now see what happens when we have x equal to c: f (c) = (c−c) q (c) + r. f (c) = (0) q (c) + r. f (c) = r. So we get this:
The remainder theorem says "when a polynomial p (x) is divided by a linear polynomial whose zero is x = k, the remainder is given by p (k)". The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder. The remainder theorem does not work when the divisor is not linear.
The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by \ [x - a\] is \ [f (a)\]. This means if \ [x - a\] is a factor of the polynomial, the remainder is zero.
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- I can't relate...it's past midnight for me... just squeezin' in some late-night studying :))
- binomial-they are with two terms polynomial-monomial,binomial,trinomial everything are considered to be a polynomial
- https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial-remainder-theorem-tutorial/v/polynomial-remainder-theorem-to-test-fact...
- It is true for x + a as well. x + a is another way of writing x - (-a). This comes into play when using synthetic division. Sometimes you'll be giv...
- x-a! buddy a=1 so we plug in one!! if it were x+a than you would be right buddie
- It would work when x has a coefficient but when you have a denominator or divisor that has a degree that's greater than one, the remainder theorem...
- of course the Theorem can be used in such cases..
- It says that if you divide a polynomial, f(x), by a linear expression, x-A, the remainder will be the same as f(A). For example, the remainder when...
- Yes, knowing the remainder can be useful. If you divide by (x-c) and have a remainder, you know that (x-c) is not a factor of the polynomial. Howev...
- you have to do polynomial long division. Your remainder will be a polynomial of degree lower than 4. You can review polynomial long division here:...
Remainder Theorem Definition. The Remainder Theorem begins with a polynomial say p (x), where “p (x)” is some polynomial p whose variable is x. Then as per theorem, dividing that polynomial p (x) by some linear factor x – a, where a is just some number.
The remainder theorem states that when we divide a polynomial p$(x)$ having a degree greater than or equal to 1 by a linear polynomial $(x − a)$, the remainder is given by r$(x) =$ p$(a)$. In simple words, if p$(x) = (x − a) q(x) + r(x)$, then $r(x) = p(a)$.
- Factor theorem helps us to check if the linear polynomial is a factor of a given polynomial.
- The remainder theorem finds its origin in the work of Chinese mathematician Sun Zi.
- If the remainder is 0, the given divisor $(x − a)$ is a factor of the dividend polynomial. In other words, it divides it exactly.
- Where $p(x)$ is the polynomial and $(x − a)$ is the divisor, we simply substitute a with $x$ and solve $p(x)$.
- No, to apply the formula, the divisor has to be a linear polynomial and cannot be a non-linear polynomial.
The remainder theorem states – if you divide a polynomial P (x) \hspace{0.2em} P(x) \hspace{0.2em} P (x) by x − a \hspace{0.2em} x - a \hspace{0.2em} x − a, the remainder would be P (a) \hspace{0.2em} P(a) \hspace{0.2em} P (a).
The Polynomial Remainder Theorem simplifies the process of finding the remainder when dividing a polynomial by \[x - a\]. Instead of long division, you just evaluate the polynomial at \[a\]. This method saves time and space, making polynomial division more manageable.
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