Answer:
If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].
Step-by-step explanation:
Let [tex]p(x) = 2\cdot x^{2}-(m+3)\cdot x - 1[/tex], if [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]p(2) = 0[/tex]. That is:
[tex]2\cdot 2^{2}-(m+3)\cdot (2)-1 = 0[/tex]
[tex]8 - 2\cdot m -6 -1 = 0[/tex]
[tex]1 -2\cdot m = 0[/tex]
[tex]2\cdot m = 1[/tex]
[tex]m = \frac{1}{2}[/tex]
If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].
