Factor 2x^2-16x+32

Problem

2*x2−16*x+32

Solution

1. Factor out the greatest common factor by identifying that each term is divisible by 2

2*(x2−8*x+16)

2. Identify the quadratic pattern inside the parentheses, noting that it is a trinomial of the form a*x2+b*x+c

x2−8*x+16

3. Find two numbers that multiply to 16 and add to −8 These numbers are −4 and −4

(−4)×(−4)=16

(−4)+(−4)=−8

4. Rewrite as a perfect square since the two factors are identical.

(x−4)*(x−4)=(x−4)2

5. Combine the results by including the greatest common factor found in the first step.

2*(x−4)2

Final Answer

2*x2−16*x+32=2*(x−4)2

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