Need help, what are the right answers?

Question

Under which conditions can the zero product property be used to solve a polynomial equation? Choose all that apply:

1. The polynomial is factored completely
2. The highest exponent in the equation is 2
3. The x coefficients cannot be fractions
4. The equation must be in standard form
5. The equation is set equal to 0

Answer 1

(1/4)(3x-2)(x+3) = 0

x=2/3, x=-3

which means you don't want the equation in standard form

standard form is: ax^2 +bx +c = 0

the x coefficents could be fractions if you hadn't factored out 1/4

then the factors could be (3x-2)(x/4+3/4)

or (3x/4 -1/2)(x+3) either which have fractional coefficients.

then set each factor equal to zero and you still get the same solutions

x=2/3, x=-3, as 3x/4-1/2=0 leads to 3x/4=1/2 and 3x=2 or x=2/3

the highest exponent doesn't have to be 2 It can be 3, 4, or more

really the only condition needed is the last, setting it equal to zero

"fully" factored isn't necessary, as the above example shows.