Question

which of the following options represents the desired result when using synthetic division to find out the upper bound of the polynomials F(x)=x^3+4x^2+x-6 ?

Answer 1

Answer:

Option (C)

Step-by-step explanation:

Given function is F(x) = x³+ 4x² + x - 6

Possible rational zeros of this function = $\frac{\pm1,\pm2,\pm3,\pm6}{\pm1}$

[Possible rational zeros of a function f(x) = ax³+ bx² + cx + d,

= $\frac{\text{factors of d}}{\text{factors of a}}$]

Let the possible zero of this function is 2.

Now do the synthetic division,

2| 1       4        1         -6

   ↓      2       12        26  

   1       6       13        20

Here all the numbers at the bottom are positive by dividing with a positive number 2, therefore, 2 is the upper bound.

There will be no rational zero (Positive) above 2.

Therefore, Option (C) will be the answer.