## Introductory Algebra for College Students (7th Edition)

The numbers $-27$ and $-19$ are negative, and they should be both positive, so the factorization is incorrect. (If both were positive, $+27$ and $+19$, then it would be correct)
If the trinomial $ax^{2}+bx+c$ can be factored, it will be in the form $(x+n)(x+m)$, where the product of integers n and m is $c$ their sum is $b.$ So if c is positive, both n and m have the same sign. If c is negative, n and m have different signs. Here, c is positive, so both n and m have the same sign. And, since b is positive, this sign must be "$+$" for both n and m. The numbers $-27$ and $-19$ are negative, and they should be both positive, so the factorization is incorrect. (If both were positive, $+27$ and $+19$, then it would be correct)