Factor 3x^2+2x-16

Problem

3*x2+2*x−16

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=3 b=2 and c=−16

2. Multiply a and c to find the product a*c=3×−16=−48

3. Find two numbers that multiply to −48 and add to the middle coefficient b=2 These numbers are 8 and −6

4. Rewrite the middle term 2*x using the two numbers found: 3*x2−6*x+8*x−16

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−2)+8*(x−2)

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

Final Answer

3*x2+2*x−16=(3*x+8)*(x−2)

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