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.
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
To determine if 2x - 3 is a factor of P(x), you need to find the value of x that makes P(x) equal to zero. If 2x - 3 is indeed a factor, then P(x) = 0 when you substitute x = 3/2, giving:
P(3/2) = 2(3/2)^3 - (3/2)^2 - 5(3/2) - 2
Simplifying this expression:
P(3/2) = 2(27/8) - 9/4 - 15/2 - 2
P(3/2) = 27/4 - 9/4 - 30/4 - 8/4
P(3/2) = (27 - 9 - 30 - 8)/4
P(3/2) = -20/4
P(3/2) = -5
Since P(3/2) is not equal to zero, 2x - 3 is not a factor of P(x) when x = 3/2.
Now, repeat the process for the other answer choices:
a. Substitute x = 3/2:
P(3/2) = -5 ≠ 0
b. Substitute x = 2/3:
P(2/3) = -6 ≠ 0
c. Substitute x = -3/2:
P(-3/2) = -11/2 ≠ 0
d. Substitute x = -2/3:
P(-2/3) = 2 ≠ 0
After evaluating P(x) for each answer choice, we find that there is no value of x that makes P(x) equal to zero. Therefore, 2x - 3 is not a factor of P(x) for any of the answer choices given.