f(x)=6xsq/ x-7 need to know the correct way too work this out. I got it wrong, not sure why

If you want to calculate the division between 6x^2
(supposing that you mean by 6xsq = 6x square raised) and x-7, you could apply the rule
of division with reminder.

Let's see
how:

6x^2 = (x-7)*Q(x) +
R(x)

Q(x) is the quotient and it is represented by a first
degree polynomial:

Q(x) =
ax+b

R(x) is the reminder and it is represented by a
constant( a number). The degree of R(x) has to be smaller that the degree of x-7. Since
the degree of the polynomial x-7 is 1, the degree of R(x) is
0.

Let's re-write the
division:

6x^2 = (x-7)*(ax+b) +
c

We'll remove the brackets from the right
side:

6x^2 = ax^2 + bx - 7ax - 7b +
c

We'll combine like terms from the right
side:

6x^2 = ax^2 + x(b-7a) - 7b +
c

The polynomial from the left side is equal with the
polynomial from the right side, if and only if the correspondent coefficients are
equal.

We'll re-write 6x^2 = 6x^2 + 0x +
0

a =
6

b - 7a = 0, but a =
6

b - 7*6 = 0

b - 42 =
0

We'll add 42 both
sides:

b =
42

-7b + c = 0, but b =
42

c = 7b

c =
7*42

c =
294

The result of the division
is :

 6x^2/(x-7) = 6x + 42 +
[294/(x-7)]