Factor 3x^2+x-4

Problem

3*x2+x−4

Solution

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

2. Multiply the leading coefficient a and the constant term c to find the product a*c=3⋅(−4)=−12

3. Find two numbers that multiply to −12 and add to the middle coefficient b=1 These numbers are 4 and −3

4. Rewrite the middle term x using the two numbers found: 4*x−3*x

3*x2+4*x−3*x−4

5. Group the terms into two pairs to perform factoring by grouping.

(3*x2−3*x)+(4*x−4)

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

3*x*(x−1)+4*(x−1)

7. Factor out the common binomial factor (x−1)

(3*x+4)*(x−1)

Final Answer

3*x2+x−4=(3*x+4)*(x−1)

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