Factor 3x^2-7x+4

Problem

3*x2−7*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−7 and c=4

2. Find two numbers that multiply to a⋅c=3⋅4=12 and add to b=−7

3. Determine the two numbers, which are −3 and −4 since (−3)*(−4)=12 and −3+(−4)=−7

4. Rewrite the middle term −7*x using the two numbers found: 3*x2−3*x−4*x+4

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−1)−4*(x−1)

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

Final Answer

3*x2−7*x+4=(3*x−4)*(x−1)

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