We have the following polynomials:
[tex]\begin{gathered} 5x^2+9x+3 \\ \\ 6x^2-3x \end{gathered}[/tex]
1. And we need to find the difference between them, and we can proceed as follows to get it:
[tex]\begin{gathered} 5x^2+9x+3 \\ -(6x^2-3x) \end{gathered}[/tex]
That is, we have to perform the next operation:
2. Now, we have to apply the distributive property - in this case, we have to multiply by -1 both terms -, and after that, we have to add algebraically the like terms as follows:
Therefore, in summary, the polynomial which represents the difference between both polynomials is:
[tex]-x^2+12x+3[/tex]
