ANSWER
[tex]a=7.5[/tex]EXPLANATION
We want to find the value of a for the given function and its factor.
Since (x - 2) is a factor of the function, it means that if 2 is substituted for x in the function, it will equate to 0.
This implies that:
[tex]\begin{gathered} F(2)=(2)^4-2(2)^3+3(2)^2-a(2)+3=0 \\ 16-16+12-2a+3=0 \\ 15-2a=0 \end{gathered}[/tex]Solve the equation for a:
[tex]\begin{gathered} 2a=15 \\ a=\frac{15}{2} \\ a=7.5 \end{gathered}[/tex]That is the value of a.
