Factor 3x^2+10x+3

Problem

3*x2+10*x+3

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅3=9 and add to b=10

3. Determine that the two numbers are 9 and 1 since 9⋅1=9 and 9 + 1 = 10$.

4. Rewrite the middle term 10*x using these two numbers: 3*x2+9*x+1*x+3

5. Factor by grouping the first two terms and the last two terms: (3*x2+9*x)+(x+3)

6. Factor out the greatest common factor from each group: 3*x*(x+3)+1*(x+3)

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

Final Answer

3*x2+10*x+3=(3*x+1)*(x+3)

Want more problems? Check here!