Factor 10x^2+17x+3

Problem

10*x2+17*x+3

Solution

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

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

3. Determine the pair of numbers, which are 15 and 2 since 15⋅2=30 and 15 + 2 = 17$.

4. Rewrite the middle term 17*x using the two numbers found: 10*x2+15*x+2*x+3

5. Factor by grouping the first two terms and the last two terms: 5*x*(2*x+3)+1*(2*x+3)

6. Factor out the common binomial (2*x+3) to obtain the final factored form.

Final Answer

10*x2+17*x+3=(5*x+1)*(2*x+3)

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