Factor 4x^2-x-3

Problem

4*x2−x−3

Solution

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

2. Calculate the product of a and c which is 4×−3=−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

4*x2−4*x+3*x−3

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

4*x*(x−1)+3*(x−1)

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

(4*x+3)*(x−1)

Final Answer

4*x2−x−3=(4*x+3)*(x−1)

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