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In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if () is a polynomial, then is a factor of () if and only if () = (that is, is a root of the polynomial).
因式定理（英語： Factor theorem ）是代数学中關於一個多項式的因式和零點的定理。 這是一個 餘式定理 的特殊情形 [ 1 ] 。 该定理指出，一個多項式 f ( x ) {\displaystyle f(x)} 有一個因式 ( a x − b ) {\displaystyle (ax-b)} 若且唯若 f ( b a ) = 0 {\displaystyle f\left({\frac ...
因式定理（英語： Factor theorem ）是代數學中關於一個多項式的因式和零點的定理。這是一個餘式定理的特殊情形 [1]。 該定理指出，一個多項式 有一個因式 若且唯若 = [2]。
- Polynomials
- The Remainder Theorem
- The Factor Theorem
- Why Is This Useful?
Well, we can also divide polynomials. f(x) ÷ d(x) = q(x) with a remainder of r(x) But it is better to write it as a sum like this: Like in this example using Polynomial Long Division(the method we want to avoid): And there is a key feature: Say we divide by a polynomial of degree 1 (such as "x−3") the remainder will have degree 0(in other words a c...
When we divide f(x) by the simple polynomial x−cwe 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: So we get this: So to find the remainder after dividing by x-cwe don't need to do any division: Just calculate f(c) Let us ...
Now ... We see this when dividing whole numbers. For example 60 ÷ 20 = 3 with no remainder. So 20 must be a factor of 60. And so we have:
Knowing that x−c is a factor is the same as knowing that c is a root (and vice versa). For one thing, it means that we can quickly check if (x−c) is a factor of the polynomial.
The factor theorem relates the factors of a given polynomial to its zeros. The factor theorem states that if f (x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f (x) if f (a) = 0.
2023年4月6日 · 因式定理（英语： Factor theorem ）是代数学中关于一个多项式的因式和零点的定理。这是一个余式定理的特殊情形 [1]。 该定理指出，一个多项式 有一个因式 当且仅当 = [2]。
In mathematics, factor theorem is used when factoring the polynomials completely. It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f (x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f (x), if f (a)=0.
