Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? select each correct answer. ±12 ±2 ±52 ±25

±2

Step-by-step explanation:

For simplicity let's take a look at a general third order polynomial:

ax^3 + bx^2 + cx + d.  In this particular case,

rational roots have the form ±d/±a.  Note that these are fractions/ratios.  Beyond that, we factor d and choose numerators ±(all possible whole number factors of d, dividing these results by all possible factors of a.

Looking at 4x^3 + 9x^2 - x + 10 = 0, we see that d = 10 and that factors of d include ±1, ±2, ±5 and ±10.  a = 4 and factors of a include ±1, ±2, ±4.

So, any rational roots of the given polynomial will stem from the possible rational roots

±1    ±2    ±5    ±10    ±1    ±2    ±5    ±10

--- , , , , , , --- , , and so on,

±1    ±1     ±1      ±1      ±2    ±2   ±2     ±2

until you have used up all of the possible factors of 10 and all of the possible factors of 4.  

Of the four possible rational roots you have shared, only ±2 (which would actually be ±2 / ±1) is acceptable.

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step-by-step explanation: