Question

How do you divide `(2x^3 +3x^2 +3x +1 ) / (2x + 1)`?

Answer 1

Quotient: `x^2 + x + 1`. Remainder : 0

Explanation:

Add and subtract suitable lower powers of x, in succession, to the terms in the numerator, so that ( 2 x + 1 ) is a factor of consecutive pairs. Then divide by ( 2 x + 1 ).

Numerator is #( 2 x^3 + x^2) + (2 x^2 + x ) + ( 2 x + 1) = ( 2 x + 1) ( x^2 + x + 1 )# .