Factor 2x^2+17x+21

Problem

2*x2+17*x+21

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=17 and c=21

2. Calculate the product of a and c which is 2×21=42

3. Find two numbers that multiply to 42 and add up to the middle coefficient b=17 These numbers are 14 and 3

4. Rewrite the middle term 17*x using the two numbers found: 14*x+3*x

2*x2+14*x+3*x+21

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

2*x*(x+7)+3*(x+7)

6. Factor out the common binomial (x+7)

(2*x+3)*(x+7)

Final Answer

2*x2+17*x+21=(2*x+3)*(x+7)

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