How many possible rational roots are there for 2x4+4x3−6x2+15x−12=0? a. 4 b. 6 c. 8 d. 12 e. 16

E. 16

Step-by-step explanation:

For this, we will use c and d to designate the values for the constant and the leading coefficient.  The possible rational roots result from the combination of both the positive and negative values found in c/d.  

First, c.  c = -12.  The factors of 12 are:

±1, ±2, ±3, ±4, ±6, ±12

Now d.  d = 2.  The factors of 2 are:

±1, ±2

Now to find the total possible rational roots we put c over d to give us:

±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2

That is 8 values, but since we have to also consider the negatives of each of them, that 8 becomes 16

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step-by-step explanation: