Factor f(x)=2x^3-4x^2-10x+20

Problem

2*x3−4*x2−10*x+20

Solution

1. Group the terms into two pairs to prepare for factoring by grouping.

(2*x3−4*x2)+(−10*x+20)

2. Factor out the greatest common factor from each pair.

2*x2*(x−2)−10*(x−2)

3. Factor out the common binomial (x−2) from the expression.

(2*x2−10)*(x−2)

4. Factor out the constant 2 from the first binomial.

2*(x2−5)*(x−2)

5. Apply the difference of squares pattern to x2−5 noting that 5=(√(,5))2

2*(x−√(,5))*(x+√(,5))*(x−2)

Final Answer

2*x3−4*x2−10*x+20=2*(x−2)*(x−√(,5))*(x+√(,5))

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