Factor 3x^2+14x-5

Problem

3*x2+14*x−5

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−5)=−15 and add to b=14

3. Determine the pair of numbers, which are 15 and −1 since 15⋅(−1)=−15 and 15 + (-1) = 14$.

4. Rewrite the middle term 14*x using these two numbers: 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 (x+5) to obtain the final factored form.

Final Answer

3*x2+14*x−5=(3*x−1)*(x+5)

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