Question

Which of the following is a factor of f(x) = 3x3 + 8x2 − 87x + 28?

Answer 1

Answer with explanation:

The expression whose factor we have to find is

   $f(x) = 3x^3 + 8x^2 - 87x + 28\\\\f(x)=3*[x^3+\frac{8x^2}{3}-29x+\frac{28}{3}]\\\\\text{By rational root test possible roots are}\\\\ \pm 1, \pm 2, \pm 4,\pm 7,\pm \frac{1}{3},\pm \frac{2}{3},\pm \frac{4}{3},\pm \frac{7}{3},\pm 28.$

First two options are rejected as the expression can,t have factor $\pm\frac{1}{4}$.

  $f(4)=3*4^3+8*4^2-87*4+28\\\\f(4)=192+128-348+28\\\\f(4)=348-348\\\\f(4)=0\\\\f(-4)=3*(-4)^3+8*(-4)^2-87*(-4)+28\\\\f(4)=-192+128+348+28\\\\f(4)\neq 0$

So, root of the expression is , x=4.

Option C: x-4

Answer 2

The answer should be (x-4)