Factor 3x^2+8x-16

Problem

3*x2+8*x−16

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=8 and c=−16

2. Find two numbers that multiply to a⋅c=3⋅(−16)=−48 and add to b=8

3. Determine the pair of numbers, which are 12 and −4 because 12⋅(−4)=−48 and 12 + (-4) = 8$.

4. Rewrite the middle term 8*x using these two numbers as 12*x−4*x

3*x2+12*x−4*x−16

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(x+4)−4*(x+4)

6. Factor out the common binomial (x+4)

(3*x−4)*(x+4)

Final Answer

3*x2+8*x−16=(3*x−4)*(x+4)

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