Factor x^2-4x+16

Problem

x2−4*x+16

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=−4 and c=16

2. Check for two numbers that multiply to a*c=16 and add to b=−4

3. Calculate the discriminant D=b2−4*a*c to determine if the expression can be factored over the real numbers.

D=(−4)2−4*(1)*(16)

D=16−64

D=−48

4. Conclude that since the discriminant is negative, the quadratic has no real roots and cannot be factored into linear factors using real numbers.

5. Complete the square if a different form is required, though the expression is considered irreducible over the integers and real numbers.

x2−4*x+4+12

(x−2)2+12

Final Answer

x2−4*x+16=Irreducible over the real numbers

Want more problems? Check here!