Can you give an example? I am intrigued, although suspect you are making a joke!
https://en.wikipedia.org/wiki/Digital_root#Properties
Example from ASVAB practice math test:
(x+4)(x+4) =
A. x^2+16x+8
B. x^2+16x+16
C. x^2+8x+16
D. x^2+8x+8
Since we don't have to solve for X in this problem, we can just assume x is 1, which would make the digital root of the problem expression 7. Assuming x = 1, the digital roots of A, B, C and D are 7, 6, 7 and 8 respectively. C is the answer because its last term is the square of 4.
You can do the same thing without the digital root. substitute 1 into all the possible answers gives: A: 25 B: 33 C: 25 D: 17
Substitute 1 into the question gives 25. Therefore only A and C are possible answers and it must be C because 4*4 = 16
This is the same process as your answer but without the digital root!
Of course there's a tiny chance that one of the other equations would be equal at your arbitrary x value. If so and you get two 'right' answers just try again with a different x.
If two polynomials evaluate to equal numbers with random variables values, the polynomials are almost certainly equal themselves
Ofc, x = 0 and x = 1 are hardly random
(x + 14284) (x + 14284)=
A: x^2 + 204032656x + 28568
B: x^2 + 204032656x + 204032656
C: x^2 + 28568x + 204032656
D: x^2 + 204032656x + 204032656
The digital root of the problem expression is 4. The digital roots of A, B, C and D are 4, 6, 4 and 3 respectively. The digital root of the square of 14284 is 1, and the digital roots of the last term of A and C are 2 and 1, respectively. The answer is C.
When a problem of this form uses big enough numbers to warrant a shortcut, digital root is almost always a suboptimal shortcut.
For example, 25 * 26 = 650, digital root 2. Or take digital root of 25 and 26 first, get 7 * 8 = 56, same digital root 2.