Factor 3x^2-4x-7

Problem

3*x2−4*x−7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−4 and c=−7

2. Find two numbers that multiply to a⋅c=3⋅(−7)=−21 and add to b=−4

3. Determine the factors of −21 that satisfy the condition: the numbers are −7 and 3

4. Rewrite the middle term −4*x using these two numbers as 3*x−7*x

3*x2+3*x−7*x−7

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

(3*x2+3*x)+(−7*x−7)

6. Factor out the greatest common factor from each group.

3*x*(x+1)−7*(x+1)

7. Factor out the common binomial (x+1)

(3*x−7)*(x+1)

Final Answer

3*x2−4*x−7=(3*x−7)*(x+1)

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