Factor 3x^2+17x+20

Problem

3*x2+17*x+20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=17 and c=20

2. Find two numbers that multiply to a⋅c and add to b

3⋅20=60

12⋅5=60

12+5=17

3. Rewrite the middle term 17*x using the two numbers found in the previous step.

3*x2+12*x+5*x+20

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

3*x*(x+4)+5*(x+4)

5. Factor out the common binomial factor (x+4)

(3*x+5)*(x+4)

Final Answer

3*x2+17*x+20=(3*x+5)*(x+4)

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