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
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:
2. (x+6) + (3x-1) = 0
We do not have a product of two terms.
The right form is:
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