Answer:
2(x+2)
Explanation:
STEPS USING DIRECT FACTORING METHOD
x
2
+4x+8
Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x
2
+Bx+C=0.
x
2
+4x+8=0
Let r and s be the factors for the quadratic equation such that x
2
+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the product of factors rs=C
r+s=−4
rs=8
Two numbers r and s sum up to −4 exactly when the average of the two numbers is
2
1
∗−4=−2. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x
2
+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. Express r and s with respect to variable u.
r=−2−u
s=−2+u
To solve for unknown quantity u, substitute these in the product equation rs=8
(−2−u)(−2+u)=8
Simplify by expanding (a−b)(a+b)=a
2
–b
2
4−u
2
=8
Simplify the expression by subtracting 4 on both sides
−u
2
=8−4=4
Simplify the expression by multiplying −1 on both sides and take the square root to obtain the value of unknown variable u
u
2
=−4
u=±
−4
=±2i
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.
r=−2−2i
s=−2+2i