Factor 2x^2+3x-5

Problem

2*x2+3*x−5

Solution

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

2. Find two numbers that multiply to a⋅c=2⋅(−5)=−10 and add to b=3

3. Determine the pair of numbers, which are 5 and −2 since 5⋅(−2)=−10 and 5 + (-2) = 3$.

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

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

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

Final Answer

2*x2+3*x−5=(2*x+5)*(x−1)

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