Answer with explanation:
The expression whose factor we have to find is
[tex]f(x) = 3x^3 + 8x^2 - 87x + 28\\\\f(x)=3*[x^3+\frac{8x^2}{3}-29x+\frac{28}{3}]\\\\\text{By rational root test possible roots are}\\\\ \pm 1, \pm 2, \pm 4,\pm 7,\pm \frac{1}{3},\pm \frac{2}{3},\pm \frac{4}{3},\pm \frac{7}{3},\pm 28.[/tex]
First two options are rejected as the expression can,t have factor [tex]\pm\frac{1}{4}[/tex].
[tex]f(4)=3*4^3+8*4^2-87*4+28\\\\f(4)=192+128-348+28\\\\f(4)=348-348\\\\f(4)=0\\\\f(-4)=3*(-4)^3+8*(-4)^2-87*(-4)+28\\\\f(4)=-192+128+348+28\\\\f(4)\neq 0[/tex]
So, root of the expression is , x=4.
Option C: x-4
