ANSWER
[tex]x - 5[/tex]
is a factor of
[tex]p(x) = 2 {x}^{2} - 7x - 15[/tex]
EXPLANATION
Set
[tex]x - 5 =0[/tex]
[tex]\Rightarrow \: x = 5[/tex]
Find
[tex]p(5)[/tex]
[tex]p(5) = 2 ({5})^{2} - 7(5) - 15[/tex]
[tex]p(5) = 2 \times 25 - 7(5) - 15[/tex]
[tex]p(5) = 50 - 35- 15[/tex]
[tex]p(5) = 15- 15[/tex]
[tex]p(5) = 0[/tex]
Since
[tex]p(5) = 0[/tex]
[tex]x - 5[/tex]
is a factor of
[tex] 2 {x}^{2} - 7x - 15[/tex]
