We want to see which equation is equivalent to the given factorized equation.
The correct option is D, the equivalent equation is:
[tex]3x^4 + 16x^3 + 3x^2 -66x - 56[/tex]
Let's solve this:
Here we have the factorized equation:
[tex](x + 1)(x - 2)(x + 4)(3x + 7)[/tex]
And we want to find a standard form equation that is equivalent to this.
To do it, we just need to expand the factorized equation by multiplying the factors.
We will get:
[tex](x + 1)(x - 2)(x + 4)(3x + 7) = (x^2 + x - 2*x - 2)(x + 4)(3x + 7) \\\\(x^2 - x - 2)*(x + 4)(3x + 7) = (x^2 - x - 2)*(3x^2 + 7x + 12x + 28)\\\\(x^2 - x - 2)*(3x^2 + 19x + 28) = 3x^4 + 19x^3 + 28x^2 - 3x^3 - 19x^2 - 28x - 6x^2 - 38x- 56\\\\= 3x^4 + 16x^3 + 3x^2 -66x - 56[/tex]
So, after the expansion, we can see that the correct option is D.
If you want to learn more, you can read:
https://brainly.com/question/10541844
