Factorize the expressions and divide them as directed:

(x² – 8x + 12) ÷ (x – 6)

In the given term

Dividend = (x² - 8x + 12)

The given expression looks as

x² + (a + b)x + ab

where a + b = -8; and ab = 12;

factors of 12 their sum

-1 × -12 -1-12 = -13

-6 × -2 -2-6 = -8

-4 × -3 -4-3 = -7

∴ the factors having sum 7 are 4 and 3

x² - 8x + 12 = x² + (-6-2)x + 12

= x² - 6x - 2x + 12

= x(x - 6) -2(x - 6)

= (x - 6)(x - 2)

Divisor = (x - 6)

=

= (x – 2)

Hence dividing (x² – 8x + 12) by (x – 6) gives out (x – 2)