Factor 4x^2-8x+3

Problem

4*x2−8*x+3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=−8 and c=3

2. Find two numbers that multiply to a⋅c=12 and add to b=−8

3. Determine the pair of numbers, which are −6 and −2 since (−6)⋅(−2)=12 and (−6)+(−2)=−8

4. Rewrite the middle term −8*x using these two numbers as −6*x−2*x

4*x2−6*x−2*x+3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*x*(2*x−3)−1*(2*x−3)

6. Factor out the common binomial (2*x−3)

(2*x−3)*(2*x−1)

Final Answer

4*x2−8*x+3=(2*x−3)*(2*x−1)

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