Factor 3x^2-14x-24

Problem

3*x2−14*x−24

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−14 and c=−24

2. Calculate the product of a and c which is 3×−24=−72

3. Find two numbers that multiply to −72 and add to the middle coefficient b=−14 These numbers are −18 and 4

4. Rewrite the middle term −14*x using the two numbers found: 3*x2−18*x+4*x−24

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−6)+4*(x−6)

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

Final Answer

3*x2−14*x−24=(3*x+4)*(x−6)

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