Factor 4x^2-4x-3

Problem

4*x2−4*x−3

Solution

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

2. Find two numbers that multiply to a⋅c=4⋅(−3)=−12 and add to b=−4

3. Determine the factors of −12 that satisfy the condition: these numbers are −6 and 2

4. Rewrite the middle term −4*x using the two numbers found: 4*x2−6*x+2*x−3

5. Factor by grouping 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) to obtain the final factored form.

Final Answer

4*x2−4*x−3=(2*x+1)*(2*x−3)

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