Question

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

(x − 1 over 4)
(x + 1 over 4)
(x − 4)
(x + 4)

Answer 1

The answer should be (x-4)

Answer 2

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+(8x^2)/(3)-29x+(28)/(3)]\\\\\text{By rational root test possible roots are}\\\\ \pm 1, \pm 2, \pm 4,\pm 7,\pm (1)/(3),\pm (2)/(3),\pm (4)/(3),\pm (7)/(3),\pm 28.`

First two options are rejected as the expression can,t have factor
`\pm(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)\\eq 0`

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

Option C: x-4