The given function is
f(x) = 27x² - 153x - 90
Factor out 9.
f(x) = 9(3x² - 17x - 10)
Note that
10 = 2*5
(3x)*5 = 15x
x*2 = 2x
-(3x)*5 - x*2 = -15x - 2x = -17x
Therefore
3x² - 17x - 10 = (3x - 2)(x - 5)
The function factors completely into
f(x) = 9(3x - 2)(x - 5)
Test the given answers.
1. 3 is a factor of 9 TRUE
2. 9 is a factor TRUE
3. x - 5 is a factor TRUE
4. x + 5 is not a factor FALSE
5. 3x - 2 is a factor TRUE
6. 3x + 2 is not a factor FALSE
7. 3x - 15 = 3(x - 5) is a factor because of 3 and (x-5) TRUE
8. 9x+6 = 3(3x+2) is not a factor because (3x+2) is not a factor FALSE
Answer:
1, 2, 3, 5 and 7 are factors.
