Factor 4x^2+7x-2

Problem

4*x2+7*x−2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=7 and c=−2

2. Calculate the product of a and c which is 4×−2=−8

3. Find two numbers that multiply to −8 and add to the middle coefficient b=7 These numbers are 8 and −1

4. Rewrite the middle term 7*x using the two numbers found: 4*x2+8*x−x−2

5. Factor by grouping the first two terms and the last two terms: 4*x*(x+2)−1*(x+2)

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

Final Answer

4*x2+7*x−2=(4*x−1)*(x+2)

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