Factor 6x^2+5x-4

Problem

6*x2+5*x−4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=5 and c=−4

2. Find two numbers that multiply to a⋅c=6⋅−4=−24 and add to b=5

3. Determine the pair of numbers, which are 8 and −3 since 8⋅−3=−24 and 8 + (-3) = 5$.

4. Rewrite the middle term 5*x using the two numbers found: 6*x2+8*x−3*x−4

5. Factor by grouping the first two terms and the last two terms: 2*x*(3*x+4)−1*(3*x+4)

6. Factor out the common binomial (3*x+4) to obtain the final factored form.

Final Answer

6*x2+5*x−4=(2*x−1)*(3*x+4)

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