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

$\begin{gathered} P(2/3)=2\cdot\frac{2}{3}-3=\frac{4}{3}-3=\frac{4-3\cdot3}{3}=\frac{4-9}{3}=-\frac{5}{3} \\ \text{This is not the binomial factor as P(2/3)}\ne0 \end{gathered}$

b. P(x)=3x-2

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

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