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What is the remainder theorem?
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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 $r(x) = p(a)$.
About. Transcript. 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.
- 4 min
- He was just plugging in _a_ (in this case, 2) for _x_. The first term of the equation is -3_x_^3. When _x_ is plugged in, it is -3*2^3, which is al...
- If you have (x+a), then the "a" value will actually be "-a" because (x+(-a))=(x-a).
- If the remainder is 0, then you know that the divisior is a factor of the dividend (they are divisble).
- With polynomial division, you can get remainders that are negative. In numeric long division, you would not have a negative remainder.
- I think that it could work. Another way to find the remainder is to set the x - a to term equal to 0 and then solve for x. After this, you just plu...
- It depends on the context of the problem (if it asks for remainder _term_); but usually, and in this problem, it should be expressed as -27, accord...
- Function of x is basically a processing machine. You give it an input, and it gives out one output and one only. For example if f(x) = x+1, you can...
- There's not much of a difference. The existence of a remainder essentially implies that if you added that value to the original equation (irrespect...
- Think about when you're dividing normal numbers that don't go into each other easily, like 9 / 4. In this problem, the remainder would only be 1. H...
May 27, 2024 · The Remainder Theorem states that if a polynomial f (x) of degree n (≥ 1) is divided by a linear polynomial (a polynomial of degree 1) g (x) of the form (x – a), the remainder of this division is the same as the value obtained by substituting r (x) = f (a) into the polynomial f (x). Mathematically,
Illustrated definition of Remainder Theorem: When we divide a polynomial f (x) by xminusc the remainder is f (c)
Remainder theorem: checking factors. Learn how to determine if an expression is a factor of a polynomial by dividing the polynomial by the expression. If the remainder is zero, the expression is a factor. The video also demonstrates how to quickly calculate the remainder using the theorem.
- 3 min
According to the polynomial remainder theorem, when you divide the polynomial function, P (x), by x-a, then the remainder will be P (a). In this case, we are dividing P (x) by x+3. x+3 can be thought of as x- (-3) and since the value "a" in the polynomial remainder has to be the constant that is being subtracted from x, our "a" value would be -3.
- 6 min
Learn to find the remainder of a polynomial using the Polynomial Remainder Theorem, where the remainder is the result of evaluating P(x) at a designated value, denoted as c.
