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 because 12⋅−2=−24 and 12 + (-2) = 10$.

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

8*x2+12*x−2*x−3

5. Factor by grouping by taking the greatest common factor out of 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)

(4*x−1)*(2*x+3)

Final Answer

8*x2+10*x−3=(4*x−1)*(2*x+3)

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