Factor 3x^2+8x+4

Problem

3*x2+8*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=8 and c=4

2. Find two numbers that multiply to a⋅c=3⋅4=12 and add up to b=8

3. Determine the factors of 12 that satisfy the condition: 6 and 2 since 6⋅2=12 and 6 + 2 = 8$.

4. Rewrite the middle term 8*x using the two numbers found: 3*x2+6*x+2*x+4

5. Factor by grouping the first two terms and the last two terms: 3*x*(x+2)+2*(x+2)

6. Factor out the common binomial (x+2) to obtain the final factored form.

Final Answer

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

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