Question

Which technique is most appropriate to use to solve each equation?

Drag the name of the technique into the box to match the equation.

Answer 1

`(x+3)(x+2)=0` ↔ zero product property and

`(x+3)(x+2)=0` ↔ square root property.

Solution:

Given expressions are
`(x+3)(x+2)=0` and
`x^(2)+6=31`.

To find which techniques is most appropriate to solve each equation.

Equation 1:
`(x+3)(x+2)=0`

Zero product property states that if AB = 0 then A = 0 or B = 0.

In the equation is
`(x+3)(x+2)=0`, zero product property is used to solve the equation.

(x + 3) = 0 (or) (x + 2) = 0

x = –3 (or) x = –2

Equation 2:
`x^(2)+6=31`

Subtract 6 from both sides of the equation.

`x^(2)+6-6=31-6`

`x^(2)=25`

`x^(2)=5^2`

Take square root on both sides of the equation.

x = 5

Square root property is used to solve the equation.

Hence
`(x+3)(x+2)=0` ↔ zero product property and

`(x+3)(x+2)=0` ↔ square root property.