At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
[tex]x^2 +4x +8\\\\= x^2 + 2 \cdot 2 \cdot x + 2^2 - 2^2 +8\\\\=(x+2)^2 - 4 +8 \\\\= (x+2)^2 +4[/tex]
Answer:
2(x+2)
Step-by-step 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
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.