Factor 5x^2+7x-6

Problem

5*x2+7*x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=7 and c=−6

2. Find two numbers that multiply to a⋅c=5⋅(−6)=−30 and add to b=7

3. Determine the pair of numbers, which are 10 and −3 because 10⋅(−3)=−30 and 10 + (-3) = 7$.

4. Rewrite the middle term 7*x using these two numbers: 5*x2+10*x−3*x−6

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

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

Final Answer

5*x2+7*x−6=(5*x−3)*(x+2)

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