Factor 12d^2+4d-1

Problem

12*d2+4*d−1

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=12 b=4 and c=−1

2. Find two numbers that multiply to a⋅c=12⋅(−1)=−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*d using the two numbers found: 12*d2+6*d−2*d−1

5. Factor by grouping the first two terms and the last two terms: (12*d2+6*d)+(−2*d−1)

6. Factor out the greatest common factor from each group: 6*d*(2*d+1)−1*(2*d+1)

7. Factor out the common binomial (2*d+1) to obtain the final factored form.

Final Answer

12*d2+4*d−1=(6*d−1)*(2*d+1)

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