Question

divide the polynomial f(x)=3x^2-x^3-3x+5 by the polynomial g(x)=x-1-x^2 and verify the division algorithm

Answer 1

hope it will help you

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

__________________________________________________

f(x) = -x³ + 3x² - 3x + 5 and g(x) = -x² + x - 1

Now, Divide it :-

-x² + x - 1  ) -x³ + 3x² - 3x + 5( x - 2

                -x³ +  x²  - x

                 -------------------------

                           2x² -  2x  +  5

                           2x²  -  2x  +  2

                            ----------------------

                                               3

                            ----------------------

We are having a quotient q(x) = x-2 and Remainder r(x) = 3

Now,

QUOTIENT × DIVISOR + REMAINDER

⇒ (x-2) ( -x²+x-1 ) + 3

⇒ -x³ + x² - x + 2x² - 2x + 2 + 3

⇒ -x³ + 3x² - 3x + 5

⇒ It's dividend ↑

$\implies\boxed{\mathsf{Hence,\:the\:division\:algorithm\:is\:verified!}}$

__________________________________________________