Factor 3x^2-x-4

Problem

3*x2−x−4

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−4)=−12 and add to b=−1

3. Determine the pair of numbers, which are −4 and 3 since (−4)⋅3=−12 and −4+3=−1

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

3*x2−4*x+3*x−4

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

x*(3*x−4)+1*(3*x−4)

6. Factor out the common binomial factor (3*x−4)

(3*x−4)*(x+1)

Final Answer

3*x2−x−4=(3*x−4)*(x+1)

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