Chapter 7 - Polynomial Equations and Factoring - 7.5 - Factoring x 2 + bx + c - Exercises - Page 389: 10

$(x-11)(x-2)$.

The given polynomial is $=x^2-13x+22$ Standard form is $x^2+bx+c$. We have $b=-13$ and $c=22$. $b$ is negative and $c$ is positive. Factor pair of $22$, whose sum is $-13$:- $-11,-2$ The values of $p$ and $q$ are $-11$ and $-2$. Hence, the factor of the polynomial is $(x+p)(x+q)=(x-11)(x-2)$. Check:- $=(x-11)(x-2)$ $=x^2-2x-11x+22$ $=x^2-13x+22$ True.