Answer :
Answer:
D, 2x - 5
Step-by-step explanation:
to solve this, you will factor the polynomial
P(x) = 2x³ - 5x² - 18x + 45 < lets break this down to factor by grouping. we will put 2x³ - 5x² in one group and -18x + 45 in another
P(x) = (2x³ - 5x²) (- 18x + 45)
lets find a common factor for 2x³ - 5x² first. a common factor is x², as both numbers have x² in them
x² (2x - 5)
now we will find a common factor of -18x + 45. both numbers are divisible by -9, so we will factor that out
-9 (2x - 5)
the polynomial now looks like the following:
P(x) = x² (2x - 5) -9 (2x - 5)
we will now create a like terms group and an unlike terms group.
x² and -9 are not alike so we will group them together, and 2x-5 are the same so we will group them together
P(x) = (x² - 9) (2x - 5) is our factored polynomial, but we are not done
x² - 9 is able to be factored into (x - 3) and (x + 3), so the polynomial becomes the following:
P(x) = (x + 3) (x - 3) (2x - 5)
to get solutions to the polynomial, we set each factor = to 0 and solve for x
x + 3 = 0 --- > x = -3
x - 3 = 0 ---> x = 3
2x - 5 = 0 ---> x = 5/2
but since the question is asking us what is a factor of the polynomial, we look back at the factors and the answers.
2x -5 is the only factor listed in the answer choices, so the answer is D, 2x - 5