Which statements are true about the polynomial 4x^3-6x^2+8x-12 Check all that apply. The terms 4x^3 and 8x have a common factor. The terms 4x^3 and -6x^2 have a common factor. D The polynomial is prime D The factored polynomial is (2x^2-3)(2x+4) D The polynomial can be grouped in different ways to factor by grouping

To determine which statements are true about the polynomial \(4x^{3}-6x^{2}+8x-12\), we will analyze each statement one by one.**Statement 1: The terms \(4x^{3}\) and \(8x\) have a common factor.**To find the common factor, we look at the coefficients and the variables separately. The coefficients are 4 and 8, which have a common factor of 4. The variables are \(x^{3}\) and \(x\), which have a common factor of \(x\). Therefore, the terms \(4x^{3}\) and \(8x\) do indeed have a common factor of \(4x\).**Statement 2: The terms \(4x^{3}\) and \(-6x^{2}\) have a common factor.**For the terms \(4x^{3}\) and \(-6x^{2}\), the coefficients are 4 and -6, which do not have a common factor other than 1. The variables are \(x^{3}\) and \(x^{2}\), which also do not have a common factor other than \(x^{2}\). Therefore, these terms do not have a common factor other than 1.**Statement 3: The polynomial is prime.**A prime polynomial is one that cannot be factored into the product of two or more non-constant polynomials with coefficients in the same field (usually the field of real numbers). We will need to check if this polynomial can be factored further.**Statement 4: The factored polynomial is \((2x^{2}-3)(2x+4)\).**To verify this factorization, we would multiply the factors to see if we get the original polynomial. However, without performing the multiplication, we cannot confirm the accuracy of this statement.**Statement 5: The polynomial can be grouped in different ways to factor by grouping.**Factoring by grouping involves rearranging and grouping terms to factor out the greatest common factor from each group. This polynomial has four terms, and we can try to group them in different ways to see if they can be factored further.**Accurate Answers:**- The terms \(4x^{3}\) and \(8x\) have a common factor. (True)- The terms \(4x^{3}\) and \(-6x^{2}\) have a common factor. (False)- The polynomial is prime. (We cannot confirm without further factoring, but it appears not to be prime based on the first two statements.)- The factored polynomial is \((2x^{2}-3)(2x+4)\). (We cannot confirm without further verification.)- The polynomial can be grouped in different ways to factor by grouping. (True)Based on the analysis, the true statements are:- The terms \(4x^{3}\) and \(8x\) have a common factor.- The polynomial can be grouped in different ways to factor by grouping.