According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 60x4 + 86x3 – 46x2 – 43x + 8?
x – 6
5x – 8
6x – 1
8x + 5
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The theorem states this:
If you have a polynomial with integer coefficients, then the list of possible rational roots is all the fractions formed by all positive or negative factors of the constant term over all positive or negative factors of the leading coefficient.
The first thing you need to do is list all factors of the constant term.
In this case, the constant term is 8.
What are all the factors of 8 (both positive and negative)?
The possible rational roots are all the fractions that can be formed using a factor of 8 as the numerator and a factor of 60 as the denominator. That gives a lot of possibilities. We don't need to check them all. We just need to look at each answer and see which answers have roots that are possible with these choices of numerators and denominators.
x - 6 = 0
Root is x = 6
There is no factor of 8 that is a 6, so you can't make a fraction equal 6, so this one is not it.
5x + 8 = 0
Root is x = -8/5
Notice that the numerator can be -8, and the denominator can be 5, so this root is possible.