Factor 4x^2-35x+49

Problem

4*x2−35*x+49

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=−35 and c=49

2. Calculate the product of a and c which is 4×49=196

3. Find two numbers that multiply to 196 and add to the middle coefficient b=−35 These numbers are −28 and −7

4. Rewrite the middle term −35*x using the two numbers found: 4*x2−28*x−7*x+49

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 4*x*(x−7)−7*(x−7)

6. Factor out the common binomial (x−7) to obtain the final factored form.

Final Answer

4*x2−35*x+49=(4*x−7)*(x−7)

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