Question

If P(2/3)=0, the binomial factor which corresponds to P(x) is:a. 2x-3b. 3x-2c. 2x+3d. 3/2

Answer 1

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

`\begin{gathered} P(2/3)=2\cdot(2)/(3)-3=(4)/(3)-3=(4-3\cdot3)/(3)=(4-9)/(3)=-(5)/(3) \\ \text{This is not the binomial factor as P(2/3)}\\e0 \end{gathered}`

b. P(x)=3x-2

`\begin{gathered} P(2/3)=3\cdot(2)/(3)-2=2-2=0 \\ \text{This is the binomial factor as P(2/3)=0} \end{gathered}`

Then the binomial factor that corresponds to P(x) is option b. 3x-2