Verified answer

x^2 - x - 12

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

....(x-4)

(x-4)(x+3)

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

...(x-4)

(x+3)

.

X^2-X-12/X-4

(X-4)(X+3)/X-4

=(X+3)

=X+3

there are 2 ways

1.the long way

substitution

we put x-4=0

x=4

then substitute this value in equation

(4)2 - 4 - 12=0 that is x-4 is its factor

then the dividend theorem

dividend = divisor *quotient +remainder

x2 - x - 12= (x-4) ?*q+0

q = x2 - x - 12 /x-4

q= x+3

2. short way

directly divide x2-x-12 by x-4

quotient -= x+3

(x^2 - x - 12)/(x - 4)

= (x^2 + 3x - 4x - 12)/(x - 4)

= [(x^2 + 3x) - (4x + 12)]/(x - 4)

= [x(x + 3) - 4(x + 3)]/(x - 4)

= (x + 3)(x - 4)/(x - 4)

= x + 3

(x^2 - x - 12) / (x - 4)

(x - 4)(x + 3) / (x 4)

(x + 3) / 1

x + 3

= (x² - x - 12)/(x - 4)

= ([x + 3][x - 4])/(x - 4)

= x + 3

Answer: x + 3

x^2-x-12

------------ =

x-4

(x-4)(x+3)

---------------- =

x-4

x+3