The expression that is a factor of the given polynomial, 2³ + 2x² - 9x - 18 is (x + 2) (option B)
How to determine which option is a factor?
According to the factor theorem, the factor of every expression will make the expression to be zero when the factor is placed in the expression.
Now, we shall use each factor from the option to see which will result to zero. This is illustrated below:
For A (x + 1)
f(x) = x³ + 2x² - 9x - 18
x + 1 = 0
x = -1
f(-1) = (-1)³ + 2(-1)² - 9(-1) - 18
= -8
For B (x + 2)
f(x) = x³ + 2x² - 9x - 18
x + 2 = 0
x = -2
f(-2) = (-2)³ + 2(-2)² - 9(-2) - 18
= 0
For C (x - 2)
f(x) = x³ + 2x² - 9x - 18
x - 2 = 0
x = 2
f(2) = (2)³ + 2(2)² - 9(2) - 18
= -20
For D (x - 6)
f(x) = x³ + 2x² - 9x - 18
x - 6 = 0
x = 6
f(6) = (6)³ + 2(6)² - 9(6) - 18
= 216
From the above, we can see that only (x + 2) makes the expression, x³ + 2x² - 9x - 18 to be zero.
Thus, the correct answer to the question is option B
Complete question:
Which expression is a factor of this polynomial?
x³ + 2x² - 9x - 18
O A. (x + 1)
O B. (x + 2)
O C. (x - 2)
O D. (x - 6)