Factor 3x^2+17x+10

Problem

3*x2+17*x+10

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=17 and c=10

2. Find two numbers that multiply to a⋅c=3⋅10=30 and add to b=17

3. Determine that the two numbers are 15 and 2 because 15⋅2=30 and 15 + 2 = 17$.

4. Rewrite the middle term 17*x using these two numbers.

3*x2+15*x+2*x+10

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

3*x*(x+5)+2*(x+5)

6. Factor out the common binomial (x+5)

(3*x+2)*(x+5)

Final Answer

3*x2+17*x+10=(3*x+2)*(x+5)

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