Which of the following could be used as justification that 3x^2+10x-8 is not prime over the set of rational numbers A. (3x+2)(x-4)B. (3x+4)(x-2)C. (3x-2)(x+4)D. (3x-4)(x+2)

Answer:CStep-by-step explanation:Consider the trinomial [tex]3x^2+10x-8.[/tex]We can rewrite it as [tex]3x^2+10x-8=3x^2+12x-2x-8.[/tex]Now group first two terms and last two terms:[tex](3x^2+12x)+(-2x-8).[/tex]The common factor in first two terms is [tex]3x[/tex] and the common factor in last two terms is [tex]-2.[/tex] Use the distributive property for both groups of terms:[tex]3x^2+12x=3x(x+4),\\ \\(-2x-8)=-2(x+4),[/tex]so[tex](3x^2+12x)+(-2x-8)=3x(x+4)-2(x+4).[/tex]Now you can see that [tex](x+4)[/tex] is a common factor, thus[tex]3x(x+4)-2(x+4)=(x+4)(3x-2)=(3x-2)(x+4).[/tex]Since the trinomial can be represented as a product of binomials, this trinomial is not prime.