For what value of x should you evaluate the polynomial P(x)=2x^3−x^2−5x−2 to determine if 2x−3 is a factor of P(x)?

a. 3/2
b. 2/3
c.-3/2
d.-2/3

can someoone please help me with this im stumped and confused.

4 answers

If 2x-3 is a factor of P(x)
then 2x-3 = 0

now solve this equation and draw your conclusion from the result
Are you sure you write the question correctly?

2 x - 3 isn't a factor of 2x³ - x² - 5 x - 2

Factorisation:

2x³ - x² - 5 x - 2 = ( x + 1 ) ( 2 x + 1 ) ( x - 2 )

Long division:

( 2x³ - x² - 5 x - 2 ) / ( 2 x - 3 ) = x² + x - 1 - 5 / ( 2 x - 3 )

This division has a remainder of - 5 so 2 x - 3 isn't a factor.
so would that mean it would -3/2?
The question did not claim that P(x)=2x^3−x^2−5x−2 has a factor of 2x-3
It asked for the value of x one should try to see if 2x-3 is a factor, that would be 3/2