Question

divide 5 x 3 - 13 x 2 + 21 x - 14 by 3- 2 X + X 2 and verify the division algorithm​

Answer 1

$f(x) = 5 {x}^{3} - 13 {x}^{2} + 21x- 14 \\ g(x) = {x}^{2} - 2x + 3$

5x - 3

x² - 2x + 3 | 5x³ - 13x² + 21x - 14

5x³ - 10x² + 15x

- 3x² - 6x - 14

- 3x² + 6x - 9

- 5

q(x) = 5x - 3

r(x) = - 5

Division Algorithm :

f(x) = g(x)*q(x) + r(x)

= [(x² - 2x + 3)*(5x - 3)] + (- 5)

= (5x³ - 10x² + 15x - 3x² + 6x - 9) + (- 5)

= 5x³ -10x² + 15x - 3x² + 6x - 9 - 5

= 5x³ -13x² + 21x - 14

Hence verified.