Question

x² - 5x + 6 ÷ x-3 using identity​

Answer 1

Answer:

x² - 5x + 6 = (x-3) (x-2) + 0 is the answer

Answer 2

$\large\underline{\sf{Given- }}$

$\: \: \: \: \: \: \: \: \bull \sf \:Evaluate \: \dfrac{ {x}^{2} - 5x + 6}{x - 3}$

$\large\underline{\sf{Solution-}}$

↝ We first factorize the numerator by using concept of splitting of middle terms.

↝ Splitting of middle terms :-

• In order to factorize  ax² + bx + c we have to find numbers p and q such that p + q = b and pq = ac.

• After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

↝ Consider

$\rm :\longmapsto\: {x}^{2} - 5x + 6$

↝Now we have to find p and q such that pq = 6 and p + q = - 5.

↝So, p and q can take the values - 2 and - 3

So,

$\rm :\longmapsto\: = \: {x}^{2} - 2x - 3x + 6$

$\rm :\longmapsto\: = \: x(x - 2) - 3(x - 2)$

$\rm :\longmapsto\: = \: (x - 2)(x - 3)$

So,

$\rm :\implies\: {x}^{2} - 5x + 6 = (x - 2)(x - 3)$

Now,

↝Consider,

$\rm :\longmapsto\:\dfrac{ {x}^{2} - 5x + 6 }{x - 3}$

$\sf \: = \dfrac{(x - 2) \: \: \cancel{(x - 3)}}{ \cancel{x - 3}}$

$\sf \: = x - 2$

$\overbrace{ \underline { \boxed { \bf \therefore \: \dfrac{ {x}^{2} - 5x + 6 }{x - 3} \: = \: x - 2}}}$

Additional Information :-

$\underline{ \boxed{ \bf {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}$

$\underline{ \boxed{ \bf {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}$

$\underline{ \boxed{ \bf {x}^{2} - {y}^{2} = (x + y)(x - y)}}$

$\underline{ \boxed{ \bf(x + a)(x + b) = {x}^{2} + (a + b)x + ab}}$