Factor 5x^2+8x+3

Problem

5*x2+8*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=8 and c=3

2. Find two numbers that multiply to a*c (which is 5×3=15 and add to b (which is 8.

3. Determine the pair of numbers, which are 3 and 5 since 3×5=15 and 3 + 5 = 8$.

4. Rewrite the middle term 8*x using these two numbers as 5*x+3*x

5*x2+5*x+3*x+3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

5*x*(x+1)+3*(x+1)

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

(5*x+3)*(x+1)

Final Answer

5*x2+8*x+3=(5*x+3)*(x+1)

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