Question

(x+2)(x+6)=0

In the problem shown, to conclude that x+2=0 or x+6=0, one must use the: A. multiplication property
B. division property
C. zero product property
D. transitive property

Answer 1

the zero product property because you can set them to 0

Answer 2

Answer: The correct option is

(C) Zero product property.

Step-by-step explanation: The given problem is

`(x+2)(x+6)=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

To conclude that x+2=0 or x+6=0, one must use which of the given properties.

We know that

for any two expressions E and F, we have

`EF=0~~~\Rightarrow E=0~\textup{or}~F=0.`

This property is known as Zero product property.

Therefore, to conclude x+2=0 or x+6=0 from the given problem (i), we must use the Zero product property.

Thus, (C) is the correct option.