Factor 3x^2-14x-5

Problem

3*x2−14*x−5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=−14 and c=−5

2. Multiply the leading coefficient a and the constant term c to find the product a*c=3⋅(−5)=−15

3. Find two numbers that multiply to −15 and add to the middle coefficient b=−14 These numbers are −15 and 1

4. Rewrite the middle term −14*x using the two numbers found: 3*x2−15*x+x−5

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

6. Factor out the common binomial factor (x−5) to obtain the final factored form.

Final Answer

3*x2−14*x−5=(3*x+1)*(x−5)

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