Factor 3x^2+8x+5

Problem

3*x2+8*x+5

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅5=15 and add up to b=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 the two numbers found: 3*x2+3*x+5*x+5

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

6. Factor out the common binomial (x+1) to obtain the final factored form.

Final Answer

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

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