Why can't the Zero Product Property be used to solve the following polynomials?

(x-2)(x)=2

(x+6)+(3x-1)=0

(x^-3)(x+7)=0

(x+9)-(6x-1)=4

(x^4)(x^2-1)=0

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1) (x-2)(x)= 2

We can not use the zero product because the product is NOT zero.

The product is 2.

In order to use the zero product, the equation must be is the format:

(x-2)(x)= 0

2. (x+6) + (3x-1) = 0

We do not have a product of two terms.

The right form is:

(x+6)(3x-1)= 0

3. x^-3 (x+7)= 0

==> (x+7)*(x^-3)= (x+7)/ x^3 = 0

Then, it is not a product of two terms. But the zero is the root of the numerator and we need to consider the domain.

4. (x^4)(x^2-1) = 0

We can use the zero product in this case.

==. x^4 (x-1) (x+1)= 0

==> x= 0, 1, and -1

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