Factor 8x^2-10x-3

Problem

8*x2−10*x−3

Solution

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

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

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

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

5. Factor by grouping the first two terms and the last two terms: 4*x*(2*x−3)+1*(2*x−3)

6. Factor out the common binomial (2*x−3) to obtain the final factored form.

Final Answer

8*x2−10*x−3=(4*x+1)*(2*x−3)

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