Remainder and Factor Theorem

Factor Theorem

( x + k ) is a factor of P ( x ) If P ( - k ) = 0

( a x + b )

Divisor P ( x ) is divided by this Also may appear in the form ( a xˆ2 + b x + c ) or even higher powers

( x + k )

Factor Also may appear in the form ( a xˆ2 + b x + c ) or even higher powers

f ( x )

Function "x" Something is done to "x", usually creating a polynomial

Remainder Theorem

P ( x ) ÷ ( a x + b ) = P ( - ( b ÷ a ) ) = R

P ( x )

Polynomial "x" An expression of more than two algebraic terms containing different powers of the same variable "x"

Q ( x )

Quotient "x" P ( x ) divided by ( a x + b ) minus R equals this It may be another polynomial as something is done to "x"

R

Remainder P ( x ) divided by ( a x + b ) minus Q ( x ) equals this It should be an expression only containing a number and no variables