Find remainder and quotient of the polynomial x4 - 9x2 + 9 when divided by x2 - 3x.
A polynomial is an algebraic expression with coefficients, variable and constants.
Answer: The remainder and quotient of the polynomial x4 - 9x2 + 9 when divided by x2 - 3x are 9 and x² + 3x respectively.
Given: Dividend = x4 - 9x2 + 9, Divisor = x2 - 3x
Let the quotient be q( x ) and remainder be r( x ).
⇒ (x4 - 9x2 + 9) ÷ (x2 - 3x)
⇒ q ( x ) = x² + 3x and r( x ) = 9
Checking the answer by using Dividend = Divisor × Quotient + Remainder
⇒ x4 - 9x2 + 9 = ( x2 - 3x ) × ( x² + 3x ) + 9
Using the identity a2 - b2 = ( a + b) ( a - b )
⇒ x4 - 9x2 + 9 = ( x2 ) 2 - ( 3x )2 + 9
LHS = RHS