Factor 5p^2-p-18

Problem

5*p2−p−18

Solution

1. Identify the coefficients of the quadratic expression in the form a*p2+b*p+c where a=5 b=−1 and c=−18

2. Calculate the product of a and c which is 5×−18=−90

3. Find two numbers that multiply to −90 and add to the middle coefficient b=−1 These numbers are −10 and 9

4. Rewrite the middle term −p using the two numbers found: −10*p+9*p

5*p2−10*p+9*p−18

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

5*p*(p−2)+9*(p−2)

6. Factor out the common binomial (p−2)

(5*p+9)*(p−2)

Final Answer

5*p2−p−18=(5*p+9)*(p−2)

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