Factor 3x^2+20x-7

Problem

3*x2+20*x−7

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=20 and c=−7

2. Find two numbers that multiply to a⋅c=3⋅(−7)=−21 and add to b=20

3. Determine the pair of numbers, which are 21 and −1 since 21⋅(−1)=−21 and 21 + (-1) = 20$.

4. Rewrite the middle term 20*x using these two numbers as 21*x−x

3*x2+21*x−x−7

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(x+7)−1*(x+7)

6. Factor out the common binomial (x+7)

(3*x−1)*(x+7)

Final Answer

3*x2+20*x−7=(3*x−1)*(x+7)

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