Factor 3x^2+4x-4

Problem

3*x2+4*x−4

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−4)=−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: 3*x2+6*x−2*x−4

5. Factor by grouping the first two terms and the last two terms: 3*x*(x+2)−2*(x+2)

6. Factor out the common binomial (x+2) to obtain the final factored form.

Final Answer

3*x2+4*x−4=(3*x−2)*(x+2)

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