To factor $\displaystyle{{x}}^{{2}}-{13}{x}+{22}\usepackage{cmbright}\Huge\$ , find integers r and s, whose product is 22 and whose sum is $\displaystyle-{13}\usepackage{cmbright}\Huge\$ . Now $\displaystyle{22}={1}\cdot{22}={2}\cdot{11}=-{1}\cdot{\left(-{22}\right)}=-{2}\cdot{\left(-{11}\right)}\usepackage{cmbright}\Huge\$ . Check each pair to find: $\displaystyle-{13}=-{2}+{\left(-{11}\right)}\usepackage{cmbright}\Huge\$ . This tells you to rewrite $\displaystyle-{13}{x}\usepackage{cmbright}\Huge\$ as $\displaystyle-{2}{x}-{11}{x}\usepackage{cmbright}\Huge\$ .