Question

apply division algorithm to find quotient and remainder .
p(x) = x^3 - 6x^2 + 11x - 6
g(x) = x^2 - 5x + 6

Answer 1

Given:-

→p(x)=x³-6x²+11x-6

→g(x)=x²-5x+6

$\rule{200}{1}$

To Find:-

→The Quotient and Remainder? -»q(x)&r(x)?

$\rule{200}{1}$

AnsWer:-

★Euclid's Division Algorithm★

→p(x)=q(x)×g(x)+r(x)

→$\frac{p(x)}{g(x)}$=q(x)+r(x)

•Putting The Values•

→$\frac{\cancel{x^{3}-6x^{2}+11x-6}}{\cancel{x^{2}-5x+6}}$=q(x)+r(x)

๛Refer Attachment๛

→q(x)=x-1

→r(x)=0

$\rule{200}{2}$

Answer 2

........

$\tt{\huge{\purple{ ................. }}}$

QUESTION :

apply division algorithm to find quotient and remainder :

p(x) = x^3 - 6x^2 + 11x - 6

g(x) = x^2 - 5x + 6

SOLUTION :

This can be done by simple division.

This is in the attachment.

For a shorter solution,

Let us try to find factors of P ( X ) by using the factor theorem

When,

X = 1, the remainder is 0

So,

( X - 1 ) is a factor.

Now, taking ( x - 1 ) common,

We get the resultant as X ^ 2 - 5x + 6

So, g(x ) comes out to be a factor of f ( x ).

For the actual method, see the attachment.