Rational Zero Theorem

Question

P(x)=35x^4+28x^3+13x^2-6x-10

I am supposed to list all possible rational zeros. HELP PLEASE!! cannot figure it out

Answer 1

First try to factor out a common number. In this case there is none.

Then find the factors of the constant which is 10

The factors of 10 are +/- 1, +/- 2, +/-5 and +/- 10

Then find the factors of the leading coefficient which is 35.

The factors of 35 are +/- 1, +/- 5, +/- 7, +/- 35

Now form all possible fractions where the numerator is a factor of 10 and the denominator is a factor of 35

So we get +/- 1, +/- 1/5, +/- 1/7, +/- 1/35, +/- 2, +/- 2/5, +/- 2/7, +/- 2/35, +/- 5, +/-5/7, +/- 10. +/- 10/7