Factor x^2+2x-4

Problem

x2+2*x−4

Solution

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

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

3. Find the roots using the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) to factor over the real numbers.

4. Substitute the values into the formula:

x=(−2±√(,2−4*(1)*(−4)))/(2*(1))

5. Simplify the expression under the radical:

x=(−2±√(,4+16))/2

x=(−2±√(,20))/2

6. Simplify the radical √(,20)=√(,4⋅5)=2√(,5)

x=(−2±2√(,5))/2

x=−1±√(,5)

7. Write the factors in the form (x−(r_1))*(x−(r_2)) where (r_1)=−1+√(,5) and (r_2)=−1−√(,5)

(x−(−1+√(,5)))*(x−(−1−√(,5)))

(x+1−√(,5))*(x+1+√(,5))

Final Answer

x2+2*x−4=(x+1−√(,5))*(x+1+√(,5))

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