Question

Solve each quadratic equation by factoring and using the zero product property.


`x^2+6x+8=0`

Answer 1

x = -4 or x = -2

Explanation:

Given equation is :

x²+6x+8 = 0

we solve above equation by factoring.

split the middle term of above equation so that the product of two terms should be 8 and the sum be 6.

x²+4x+2x+8 = 0

make two groups

x(x+4)+2(x+4) = 0

take (x+4) as common

(x+4)(x+2) = 0

Applying Zero-Product Property to above equation ,we get

x+4 = 0 or x+2 = 0

If x+4 = 0

adding -4 to both sides of above equation, we get

x+4-4 = 0-4

x+0 = -4

x = -4

If x+2 = 0

adding -2 to both sides of above equation,we get

x+2-2 = 0-2

x+0 = -2

x = -2

hence, the solution of x²+6x+8 = 0 is {-4,-2}.

Answer 2

x=-4 x=-2

Explanation:

x^2+6x+8=0

What 2 numbers multiply to give us 8 and add to give us 6

4*2 = 8 4+2 =6

(x+4) (x+2) =0

Using the zero product property

x+4 =0 and x+2 =0

x+4-4 = 0-4 x+2-2 = 0-2

x=-4 x=-2