Factor 4x^2+5x-6

Problem

4*x2+5*x−6

Solution

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

2. Find two numbers that multiply to a⋅c=4⋅(−6)=−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: 4*x2+8*x−3*x−6

5. Factor by grouping the first two terms and the last two terms: (4*x2+8*x)+(−3*x−6)

6. Factor out the greatest common factor from each group: 4*x*(x+2)−3*(x+2)

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

Final Answer

4*x2+5*x−6=(4*x−3)*(x+2)

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