You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
Any rational number can be used in the remainder theorem: 4 does not have a special role.
euclid
Euclid
you
he dicovered it in greece
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
Remainder Theorem:- When f(x) is divided by (x-a) the remainder is f(a) Tor example:- f(x) x3-2x2+5x+8 divided by x-2 f(2) 8-8+10+8 = 18 So the remainder is 18 if there is no remainder then the divisor is a factor of the dividend.
F(a)
The remainder is not zero so y-3 is not a factor of y^4+2y^2-4
If a polynomial is divided by x - c, we can use the Remainder theorem to evaluate the polynomial at c.The Remainder theorem:If the polynomial f(x) is divided by x - c, then the remainder is f(c).Example:Given f(x) = x^3 - 4x^2 + 5x + 3, use the remainder theorem to find f(2).Solution:By the remainder theorem, if f(x) is divided by x - 2, then the remainder is f(2).We can use the synthetic division to divide.2] 1 -4 5 32 -4 2__________1 -2 1 5The remainder is 5, so f(2) = 5Check:f(x) = x^3 - 4x^2 + 5x + 3f(2) = (2)^3 - 4(2)^2 + 5(2) + 3 = 8 - 16 + 10 + 3 = 5