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

$(x+9)(x-7)$
The given expression, $2x-63+x^2 ,$ is equivalent to $x^2+2x-63.$ Using the factoring of trinomials in the form $x^2+bx+c,$ the value of $c$ is $-63$ and the value of $b$ is $2 .$ The two numbers that have a product of $c$ and a sum of $b$ are $\{9,-7\} .$ Hence, the factored form of the expression above is \begin{array}{l}\require{cancel} (x+9)(x-7) .\end{array}