Question

Apply the division algorithm to find the quotient and remainer on dividing f(x) by g(x) ,f(x)=x^3-3x^2+5x-3,g(x)= x^2-2

Answer 1

I think it will help you.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

f(x) = x^3 - 3x^2 + 5x - 3

g(x) = x^2 - 2

(x^3 - 3x^2 + 5x - 3) = q(x).(x^2 - 2) + r(x)

Degree of g(x) = 2

So

r(x) must be degree less than 2

(x^3 - 3x^2 + 5x - 3) = (ax + b)(x^2 - 2) + (cx + d)

(x^3 - 3x^2 + 5x - 3) = ax^3 + bx^2 + (-2a + c)x + (-2b + d)

★Coefficient we get :-

1 = a

-3 = b

5 = -2a + c

-3 = -2b - 3 = -9

★Quotient = x - 3

★Remainder = 7x - 9