Factor x^2+4x+6

Problem

x2+4*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=1 b=4 and c=6

2. Calculate the discriminant to determine if the quadratic can be factored over the real numbers using the formula D=b2−4*a*c

3. Substitute the values into the discriminant formula: D=4−4*(1)*(6)=16−24=−8

4. Conclude that since the discriminant is negative (D<0, the quadratic has no real roots and cannot be factored into linear factors with real coefficients.

5. Complete the square to express the quadratic in vertex form if an alternative representation is needed.

6. Apply the completing the square method: x2+4*x+4−4+6=(x+2)2+2

Final Answer

x2+4*x+6=(x+2)2+2

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