Factor 8x^2+2x-3

Problem

8*x2+2*x−3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=8 b=2 and c=−3

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

3. Determine the pair of numbers, which are 6 and −4 since 6⋅(−4)=−24 and 6 + (-4) = 2$.

4. Rewrite the middle term 2*x using the two numbers found: 8*x2+6*x−4*x−3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(4*x+3)−1*(4*x+3)

6. Factor out the common binomial (4*x+3) to obtain the final factored form.

Final Answer

8*x2+2*x−3=(2*x−1)*(4*x+3)

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