Factor x^2-4x-4

Problem

x2−4*x−4

Solution

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

2. Check for integer factors of a*c=−4 that sum to b=−4 Since the factors of −4 are (1,−4) (−1,4) and (2,−2) none of which sum to −4 the expression cannot be factored using integers.

3. Apply the quadratic formula to find the roots by solving x2−4*x−4=0

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula.

x=(4±√(,(−4)2−4*(1)*(−4)))/(2*(1))

5. Simplify the discriminant and the expression.

x=(4±√(,16+16))/2

x=(4±√(,32))/2

x=(4±4√(,2))/2

x=2±2√(,2)

6. Write the factored form using the roots (r_1)=2+2√(,2) and (r_2)=2−2√(,2) in the form (x−(r_1))*(x−(r_2))

(x−(2+2√(,2)))*(x−(2−2√(,2)))

Final Answer

x2−4*x−4=(x−2−2√(,2))*(x−2+2√(,2))

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