We want to multiply two polynomials of degree 1, and get in that way a polynomial of degree 2.
We will get the polynomial: [tex]p(x) = 2*x^2 + 2*x - 12[/tex]
--------------------------------
We just want to multiply (x + 3) and (2*x - 4).
So we start by writing:
[tex](x + 3)*(2*x - 4)[/tex]
Now we just expand this:
[tex](x + 3)*(2*x - 4) = 2*x^2 + x*(-4) + 3*(2*x) + 3*(-4)[/tex]
Now we need to simplify the above expression:
[tex]2*x^2 + x*(-4) + 3*(2*x) + 3*(-4) = 2*x^2 + (6 - 4)*x - 12[/tex] [tex]= 2*x^2 + 2*x - 12[/tex]
This is the polynomial we wanted to get:
[tex]p(x) = 2*x^2 + 2*x - 12[/tex]
If you want to learn more, you can read:
https://brainly.com/question/11536910
