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 factors of −24 that satisfy the condition, which are −12 and 2

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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