Factor 3x^2+4x-7

Problem

3*x2+4*x−7

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−7)=−21 and add to b=4

3. Determine the factors of −21 that satisfy the condition: 7 and −3 since 7⋅(−3)=−21 and 7 + (-3) = 4$.

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

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−1)+7*(x−1)

6. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

3*x2+4*x−7=(3*x+7)*(x−1)

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