Chapter 10 - Section 10.6 - Factoring General Trinomials - Exercise - Page 356: 27

$-(3c+10)(c-9)$

For the polynomial $$ -3c^2 +17c +90=-(3c^2 -17c -90) $$ we check the factors of $ac=3(-90)=-270$. The only factors that can give the right middle term are $10$ and $-27$, as follows $$ -3c^2 +17c +90=-(3c^2 -17c -90)=-(3c+10)(c-9) .$$