how to factor then solve this problem

Question

x²+6x+8=0

Answer 1

Given expression is x² + 6x + 8

 

To break this into factors, we need to find 2 numbers such that the product of the two numbers is 8 (the constant or the term without X) and the sum of the 2 numbers is 6 (the coeff of x)

 

we have 2 such numbers ....2 and 4

 

we rewrite the expression as 

 

x² + (4+2)x + 4*2

 

= x² + 4x + 2x + 4*2

 

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

 

= (x+4) (x+2) ..............................This step we are taking (x+4) common in the expression

 

So we have now factors for the expression.

 

To solve the equation

 

x2 + 6x + 8 = 0 

is same as solving (x+2)(x+4) = 0

 

If product of 2 numbers is zero, then one of them should be zero

so either x+2 = 0 or x+4 =0

so x = -2 or -4