Factor 3x^2+2x-5

Problem

3*x2+2*x−5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=2 and c=−5

2. Find two numbers that multiply to a⋅c=3⋅(−5)=−15 and add to b=2

3. Determine the factors of −15 that satisfy the condition: 5 and −3 since 5⋅(−3)=−15 and 5 + (-3) = 2$.

4. Rewrite the middle term 2*x using the two numbers found: 3*x2−3*x+5*x−5

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

6. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

3*x2+2*x−5=(3*x+5)*(x−1)

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