Use the Factor Theorem to determine whether x-3 is a factor of P(x)=2x^3-5x^-9 .
Specifically, evaluate P at the proper value, and then determine whether x-3 is a factor.
P(_)=__
also pick which one applies
x-3 is not a factor of P(x)
x-3 is a factor of P(x)
It was P(x)=2x^3-5x^2-9 I got 0 and x-3 is a factor
To determine whether x-3 is a factor of P(x) = 2x^3 - 5x^-9 using the Factor Theorem, you need to follow these steps:
Step 1: Evaluate P at the proper value:
Replace every instance of 'x' in P(x) with '3' to calculate P(3):
P(3) = 2(3)^3 - 5(3)^-9
P(3) = 2(27) - 5(1/729)
P(3) = 54 - 5/729
Simplifying further, we get:
P(3) = 54 - 5/729
Step 2: Determine whether x-3 is a factor of P(x):
If P(3) equals zero, then x-3 is a factor of P(x). Otherwise, x-3 is not a factor.
Comparing P(3) with zero, we have:
54 - 5/729 = 0
If the result is true, then x-3 is a factor of P(x). If the result is false, then x-3 is not a factor.
In this case, 54 - 5/729 ≠ 0, which means x-3 is not a factor of P(x). Therefore, the correct answer is: x-3 is not a factor of P(x).
Please note that since P(x) is an equation with exponents and fractions, it is important to simplify when evaluating P(3).