If P(2/3)=0 then when x=2/3, the function P(x)=0
Then, replace the x-value by 2/3 and let's find out which function is equal to 0.
a. P(x)=2x-3
[tex]\begin{gathered} P(2/3)=2\cdot\frac{2}{3}-3=\frac{4}{3}-3=\frac{4-3\cdot3}{3}=\frac{4-9}{3}=-\frac{5}{3} \\ \text{This is not the binomial factor as P(2/3)}\ne0 \end{gathered}[/tex]b. P(x)=3x-2
[tex]\begin{gathered} P(2/3)=3\cdot\frac{2}{3}-2=2-2=0 \\ \text{This is the binomial factor as P(2/3)=0} \end{gathered}[/tex]Then the binomial factor that corresponds to P(x) is option b. 3x-2