Question

Which technique is most appropriate to use to solve each 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.