Factor x^2+4x+2

Problem

x2+4*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=4 and c=2

2. Check for integer factors by looking for two numbers that multiply to a*c=2 and add to b=4 Since no such integers exist, the expression cannot be factored over the integers.

3. Complete the square to find the roots or factor over the real numbers. To complete the square, take half of b which is 2 and square it to get 4

4. Rewrite the expression by adding and subtracting 4

x2+4*x+4−4+2

5. Group the perfect square trinomial:

(x+2)2−2

6. Apply the difference of squares formula a2−b2=(a−b)*(a+b) treating 2 as (√(,2))2

(x+2−√(,2))*(x+2+√(,2))

Final Answer

x2+4*x+2=(x+2−√(,2))*(x+2+√(,2))

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