Factor 3x^2+4x+1

Problem

3*x2+4*x+1

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=4 and c=1

2. Find two numbers that multiply to a⋅c=3⋅1=3 and add to b=4

3. Determine the pair of numbers, which are 3 and 1 since 3⋅1=3 and 3 + 1 = 4$.

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

5. Factor by grouping the first two terms and the last two terms: 3*x*(x+1)+1*(x+1)

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

Final Answer

3*x2+4*x+1=(3*x+1)*(x+1)

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