If 3x² + 2x +4 is a factor of polynomial
9x⁴ + 12x³ + 28x² + nx + m, find the values of m and n.

As per the reply I recieved earlier for this question, I solved it on my own and got the following answers:-
m=16 and n=16

Could you please check the answers and tell if it is correct or not. If it is not correct then please send the answer in a step by step.

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Solution

The answer is correct.
You could, in fact, see that with the values of n and m substituted, the polynomial is the square of 3x^2+2x+4
i.e., 9x^4+12x^3+28x^2+16x+16= (3x^2+2x+4)^2

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The answer is correct. You could, in fact, see that with the values of n and m substituted, the polynomial is the square of 3x^2+2x+4 i.e., 9x^4+12x^3+28x^2+16x+16= (3x^2+2x+4)^2

The answer is correct.
You could, in fact, see that with the values of n and m substituted, the polynomial is the square of 3x^2+2x+4
i.e., 9x^4+12x^3+28x^2+16x+16= (3x^2+2x+4)^2