is 2x-3 a factor of 4x^2+9-12x?

by factor theorem,
x=3/2
f(x)=3+9-6=0
since the remainder is 0 hence 2x-3 is the factor

2x - 3 = 2 (x - 3/2)
If 2x - 3 is a factor, x - 3/2 has to divide exactly into 4x² - 12x + 9 leaving no remainder.
Try synthetic division :-
3/2 | 4 ____-12____9
_ _ |_______6____-9
_ _ | 4_____-6____0 = R

R = 0 thus 2x - 3 is a factor.

4x^2 + 9 - 12x
= 4x^2 - 12x + 9
= (2x - 3)(2x - 3)
= (2x - 3)^2

Yes, your answer is correct.

Long division. If no remainder, then it's a factor. If you're not familiar with long division, then do the following.

2x-3 = 0
x = 3/2
Substitute x=3/2 into the equation, if it all sums up to 0, then it is a factor.

yes (2x-3)^2=4x^2+9-12x

YES
coz
4x^2-12x+9 =(2x-3)^2

a^2-2ab+b^2= (a-b) ^2 =>so (a-b) is a factor of a^2-2ab+b^2