Factor 4x^2+11x+6

Problem

4*x2+11*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=11 and c=6

2. Calculate the product of a and c which is 4×6=24

3. Find two numbers that multiply to 24 and add up to the middle coefficient b=11 These numbers are 8 and 3

4. Rewrite the middle term 11*x using the two numbers found: 8*x+3*x

4*x2+8*x+3*x+6

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

4*x*(x+2)+3*(x+2)

6. Factor out the common binomial factor (x+2)

(4*x+3)*(x+2)

Final Answer

4*x2+11*x+6=(4*x+3)*(x+2)

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