Question

Divide 6x³-11x²+7x+5 by 2x-3 and verify division algorithm

Answer 1

Given :-

p(x) = 6x³- 11x² + 7x + 5

g(x) = 2x - 3

Refer attachment for division.

Verifying using division algorithm :-

Divident = Divisor x Quotient + Remainder

p(x) = g(x) x q(x) + r(x)

LHS = 6x³- 11x² + 7x + 5

RHS = (2x - 3)(3x² - x + 2) + 11

= 6x³ - 2x² + 4x - 9x² + 3x - 6 + 11

= 6x³ - 11x² + 7x + 5

LHS = RHS

- Hence verified.

Answer 2

Given :

◾Divide 6x³-11x²+7x+5 by 2x-3 and verify division algorithm

Solution :

ᏴᎽ ᎠᏆᏙᏆᎠᏆΝᏀ, ᏔᎬ ᏀᎬͲ :-

◾3x²- x +2

ᏙᎬᎡᏆҒᏆᏟᎪͲᏆϴΝ :-

Divident = Divisor x Quotient + Remainder

p(x) = g(x) x q(x) + r(x)

LHS = 6x³- 11x² + 7x + 5

RHS = (2x - 3)(3x² - x + 2) + 11

= 6x³ - 2x² + 4x - 9x² + 3x - 6 + 11

= 6x³ - 11x² + 7x + 5

${\therefore}$LHS = RHS

- Hence verified.