explain the remainder theorem
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.. The remainder theorem states the following: If you divide a polynomial f(x) by (x - h), then the remainder is f(h). The theoremstates that our remainder equals f(h). Therefore, we do not need to use long division, but just need to evaluate the polynomial when x = h to find theremainder.
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☛ Factor Theorem ;
If p ( x ) is a polynomial of degree ≥ one and a is any real number , then
( i ) ( x - a ) is a factor of p ( x ) , if p ( a ) = 0.
( ii ) p ( a ) = 0, if ( x - a ) is a factor of p (x).
☛ Remainder Theorem ;
Division and Algorithm for polynomials : If p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find q ( x ) and r (x) and such that
p ( x ) = g ( x ) * q ( x ) + r ( x ), where
r (x) = 0 (or) deg r(x) < deg g(x)
Dividend = Divisor × quotient + remainder
If p ( x ) is a polynomial of degree ≥ one and a is any real number , then
( i ) ( x - a ) is a factor of p ( x ) , if p ( a ) = 0.
( ii ) p ( a ) = 0, if ( x - a ) is a factor of p (x).
☛ Remainder Theorem ;
Division and Algorithm for polynomials : If p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find q ( x ) and r (x) and such that
p ( x ) = g ( x ) * q ( x ) + r ( x ), where
r (x) = 0 (or) deg r(x) < deg g(x)
Dividend = Divisor × quotient + remainder
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