Factor 10x^2+13x-3

Problem

10*x2+13*x−3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=10 b=13 and c=−3

2. Find two numbers that multiply to a*c=10⋅(−3)=−30 and add to b=13

3. Determine the pair of numbers, which are 15 and −2 since 15⋅(−2)=−30 and 15 + (-2) = 13$.

4. Rewrite the middle term 13*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+13*x−3=(5*x−1)*(2*x+3)

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