## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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