Factor 3p^2-2p-5

Problem

3*p2−2*p−5

Solution

1. Identify the coefficients of the quadratic expression in the form a*p2+b*p+c where a=3 b=−2 and c=−5

2. Find two numbers that multiply to a*c=3×−5=−15 and add to b=−2

3. Determine that the two numbers are −5 and 3 since −5×3=−15 and −5+3=−2

4. Rewrite the middle term −2*p using these two numbers as −5*p+3*p

3*p2−5*p+3*p−5

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

p*(3*p−5)+1*(3*p−5)

6. Factor out the common binomial (3*p−5)

(3*p−5)*(p+1)

Final Answer

3*p2−2*p−5=(3*p−5)*(p+1)

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