Factor 2x^2+7x-4

Problem

2*x2+7*x−4

Solution

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

2. Find two numbers that multiply to a⋅c=2⋅(−4)=−8 and add to b=7

3. Determine the pair of numbers, which are 8 and −1 since 8⋅(−1)=−8 and 8 + (-1) = 7$.

4. Rewrite the middle term 7*x using these two numbers:

2*x2+8*x−x−4

5. Factor by grouping the first two terms and the last two terms:

2*x*(x+4)−1*(x+4)

6. Factor out the common binomial (x+4)

(2*x−1)*(x+4)

Final Answer

2*x2+7*x−4=(2*x−1)*(x+4)

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