SOLUTION: Please help me, I'm so confused! List the possible rational zeros of the function using the rational zero theorem. a) f(x)= x^4 - 6x^3 + 8x^2 - 21 b) h(x)= 5x^4 + 12x^3

SOLUTION: Please help me, I'm so confused! List the possible rational zeros of the function using the rational zero theorem. a) f(x)= x^4 - 6x^3 + 8x^2 - 21 b) h(x)= 5x^4 + 12x^3 - 16

Question 147621: Please help me, I'm so confused!
List the possible rational zeros of the function using the rational zero theorem.
a) f(x)= x^4 - 6x^3 + 8x^2 - 21
b) h(x)= 5x^4 + 12x^3 - 16x^2 + 10
c) g(x)= 9x^5 + 3x^3 + 7x - 4
Find all real zeros of the function.
g(x)= x^3 + 4x^2 - x - 4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started.

a)

Any rational zero can be found through this equation

where p and q are the factors of the last and first coefficients

So let's list the factors of -21 (the last coefficient):

Now let's list the factors of 1 (the first coefficient):

Now let's divide each factor of the last coefficient by each factor of the first coefficient

Now simplify

These are all the distinct rational zeros of the function that could occur

b)

Any rational zero can be found through this equation

where p and q are the factors of the last and first coefficients

So let's list the factors of 10 (the last coefficient):

Now let's list the factors of 5 (the first coefficient):

Now let's divide each factor of the last coefficient by each factor of the first coefficient

Now simplify

These are all the distinct rational zeros of the function that could occur

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