Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 29

$(y+9)(y-5)$

In decreasing order of exponents, the given expression, $ 4y-45+y^2 ,$ is equivalent to \begin{array}{l} y^2+4y-45 .\end{array} The 2 numbers whose product is $ac= 1(-45)=-45 $ and whose sum is $b= 4 $ are $\left\{ 9,-5 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} y^2+9y-5y-45 \\\\= (y^2+9y)-(5y+45) \\\\= y(y+9)-5(y+9) \\\\= (y+9)(y-5) .\end{array}