Question

1) if the polynomial p(x) has factories of 12, (x-5), and (x+4), which of the following must also be a factor of p(x)?

2x^2 + 8
4x^2-20
6x^2 -6x-120
x^2-10x+25

2) IF f(x)= -x+7 and g(f(x))= 2x+1, what is the value of g(2)?

^I got 11

The square of a positive number is .24 greater than the number itself. What is that number?

Answer 1

Hmmm. Never heard of polynomial factories. So, assuming you meant factors,

If (x-5) and (x+4) are factors, so is
(x-5)(x+4) = x^2-x-20

That's not one of the choices, but if 12 is also a factor, so is 6. Now what do you say?

since f(5) = 2,
g(2) = g(f(5)) = 2*5+1 = 11
good job

x^2 = x + .24
x^2-x-.24 = 0
x = 1.2
check: 1.2^2 = 1.44 = 1.2+.24

Answer 2

polynomials have factors, not factories ....

we could write the factors of p(x) as
2*2*3*(x-5)*(x+4)

any combination of these will also be a factor.
How about 2*3*(x-5)(x+4)
expand it and see what you get

2) correct

3)
x^2 - x = .24
x^2 - x -.24 = 0
solve for x using the quadratic formula