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21 Νοε 2023 · The remainder theorem relates the values of a polynomial to its remainders when divided using those points. The factor theorem is a specific case: if P (a) = 0, then the remainder of P (x) / (x...
What is the remainder theorem? The remainder theorem states that if you want to find f (x) of any function, you can synthetically divide by whatever "x" is, get the remainder and you will have the corresponding "y" value. Lets go through an example: (I have to assume you know synthetic division)
1 Νοε 2023 · The Remainder theorem tells: For every x on [c−d,c+ d] the error term satisfies the bound |f(x) −P n(x)|≤M (n+1) (x−c)n+1 (n+ 1)! Example: For f(x) = ex and c = 0 we have R n(x) = ex (x−0)n+1 (n+ 1)!. For x = 1, this gives the bound R n(1) = e/(n + 1)! which for n = 5is R 5(1) = e/720 = 0.00377. The actual error is e −(1 + 1 + 1/2 ...
21 Νοε 2023 · How can one solve polynomial division for a remainder? As an example, given a polynomial function f, we can evaluate f (x) at x = k by using the Remainder Theorem. First, use synthetic...
The remainder theorem is used to find the remainder without using the long division when a polynomial is divided by a linear polynomial. It says when a polynomial p(x) is divided by (x - a) then the remainder is p(a).
15 Αυγ 2023 · Use the Factor Theorem to factor a polynomial into the product of linear and irreducible quadratic factors. Use the Remainder and Factor Theorems, possibly with synthetic division, to determine the value of a polynomial. Use synthetic division to find the remainder when a polynomial is divided by a linear expression.
The Remainder Theorem: When we divide a polynomial f (x) by x−c the remainder is f (c) So to find the remainder after dividing by x-c we don't need to do any division: Just calculate f (c) Let us see that in practice: Example: The remainder after 2x 2 −5x−1 is divided by x−3.
