This is an irreducible quadratic. The constant, by multiplying the first and last terms. In this equation, it is found like this: 9 ∗ − 10 = − 90 Now, in order for it to be factored, two factors of − 90 must be equal to − 5 .
Since there are no two factors of − 90 that equal − 5 , this is an irreducible quadratic.
The quadratic 9 r 2 − 5 r − 10 cannot be factored neatly into rational factors. Using the quadratic formula, we see it has roots that are not integers, indicating the expression is irreducible. Therefore, it does not factor over the rational numbers.
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