To factor $\displaystyle{{x}}^{{2}}-{3}{x}-{28}\usepackage{cmbright}\Huge\$ , find integers r and s, whose product is $\displaystyle-{28}\usepackage{cmbright}\Huge\$ and whose sum is $\displaystyle-{3}\usepackage{cmbright}\Huge\$ .

$\displaystyle-{28}={1}\cdot{\left(-{28}\right)}={2}\cdot{\left(-{14}\right)}={4}\cdot{\left(-{7}\right)}=-{1}\cdot{28}=-{2}\cdot{14}=-{4}\cdot{7}\usepackage{cmbright}\Huge\$

Check each pair to find: $\displaystyle-{3}={4}+{\left(-{7}\right)}\usepackage{cmbright}\Huge\$ . This tells you to rewrite $\displaystyle-{3}{x}\usepackage{cmbright}\Huge\$ as $\displaystyle{4}{x}-{7}{x}\usepackage{cmbright}\Huge\$ .