Factor 3x^2+10x-8

Problem

3*x2+10*x−8

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=10 and c=−8

2. Find two numbers that multiply to a⋅c=3⋅(−8)=−24 and add to b=10

3. Determine the pair of numbers, which are 12 and −2 because 12⋅(−2)=−24 and 12 + (-2) = 10$.

4. Rewrite the middle term 10*x using these two numbers: 3*x2+12*x−2*x−8

5. Factor by grouping the first two terms and the last two terms: 3*x*(x+4)−2*(x+4)

6. Factor out the common binomial (x+4) to obtain the final factored form.

Final Answer

3*x2+10*x−8=(3*x−2)*(x+4)

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