Factor 4x^2+4x-3

Problem

4*x2+4*x−3

Solution

1. Identify the coefficients of the quadratic expression 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 pair of numbers, which are 6 and −2 since 6⋅(−2)=−12 and 6 + (-2) = 4$.

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)

Final Answer

4*x2+4*x−3=(2*x+3)*(2*x−1)

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