Question

Divide 2x³+3x²+5x+6 by x²+3x+2. Find the quotient and remainder and verify the division algorithm
Pls answer

Answer 1

After dividing 2x^3 + 3x^2 + 5x + 6 from x^2 + 3x + 2

we will get

dividend -> x^2 + 3x + 2

divisor -> 2x^3 + 3x^2 + 5x + 6

remainder -> 10x + 12

quotient -> 2x - 3

to verify division algorithm :-

2x^3 + 3x^2 + 5x + 6 = ( x^2 + 3x + 2) (2x -3) × 10x + 12

solving RHS

( x^2 + 3x + 2) (2x -3) × 10x + 12

=2x^3 + 6x^2 + 4x - 3x^2 - 9x - 6 + 10x + 12

= 2x^3 + 3x^2 + 5x + 6

here, LHS = RHS

hence verified