Factor 4x^2-17x+4

Problem

4*x2−17*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=−17 and c=4

2. Calculate the product a*c which is 4×4=16

3. Find two numbers that multiply to 16 and add to the middle coefficient b=−17 These numbers are −16 and −1

4. Rewrite the middle term −17*x using the two numbers found: −16*x−x

4*x2−16*x−x+4

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

(4*x2−16*x)−(x−4)

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

4*x*(x−4)−1*(x−4)

7. Factor out the common binomial (x−4)

(4*x−1)*(x−4)

Final Answer

4*x2−17*x+4=(4*x−1)*(x−4)

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