Factor 8x^2+10x+3

Problem

8*x2+10*x+3

Solution

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

2. Calculate the product of a and c which is 8⋅3=24

3. Find two numbers that multiply to 24 and add up to the middle coefficient b=10 These numbers are 4 and 6

4. Rewrite the middle term 10*x using the two numbers found: 4*x+6*x

8*x2+4*x+6*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+1)+3*(2*x+1)

6. Factor out the common binomial factor (2*x+1)

(2*x+1)*(4*x+3)

Final Answer

8*x2+10*x+3=(2*x+1)*(4*x+3)

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