what is factor theorem and remainder theorem explain in details the statement
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factor theorem the algebra the factor theorem is a theorem linking factor and zeros of polynomials it is a special case of the remainder theorem the factor theorem stays that are polynomials has sector if and only if
remainder theorem in Algebra the polynomials remind theorem of little bezouts theorem is an application of Euclid division of polynomials its States that the reminder of the division of a polynomials by a linear polynomials is equal
remainder theorem in Algebra the polynomials remind theorem of little bezouts theorem is an application of Euclid division of polynomials its States that the reminder of the division of a polynomials by a linear polynomials is equal
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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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