Factor x^2+4x+1

Problem

x2+4*x+1

Solution

1. Identify the quadratic expression x2+4*x+1 which is in the form a*x2+b*x+c where a=1 b=4 and c=1

2. Check for simple integer factors. Since no two integers multiply to 1 and add to 4 we use the method of completing the square.

3. Complete the square by taking half of the linear coefficient b=4 which is 2 and squaring it to get 4

4. Rewrite the expression by adding and subtracting 4 to maintain equality.

x2+4*x+4−4+1

5. Group the perfect square trinomial and simplify the remaining constants.

(x+2)2−3

6. Apply the difference of squares formula a2−b2=(a−b)*(a+b) treating 3 as (√(,3))2

(x+2−√(,3))*(x+2+√(,3))

Final Answer

x2+4*x+1=(x+2−√(,3))*(x+2+√(,3))

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