Factor 20x^3-8x^2-5x+2

Problem

20*x3−8*x2−5*x+2

Solution

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

(20*x3−8*x2)+(−5*x+2)

2. Factor out the greatest common factor from the first pair, which is 4*x2

4*x2*(5*x−2)+(−5*x+2)

3. Factor out a negative one from the second pair to make the binomial terms match.

4*x2*(5*x−2)−1*(5*x−2)

4. Factor out the common binomial (5*x−2) from the expression.

(5*x−2)*(4*x2−1)

5. Identify the difference of squares in the second factor, noting that 4*x2−1=(2*x)2−1

(5*x−2)*(2*x−1)*(2*x+1)

Final Answer

20*x3−8*x2−5*x+2=(5*x−2)*(2*x−1)*(2*x+1)

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