Question

Factorice p^2-15p+54

Answer 1

Step-by-step explanation:

Factor the expression by grouping. First, the expression needs to be rewritten as p

2

+ap+bp+54. To find a and b, set up a system to be solved.

a+b=15

ab=1×54=54

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 54.

1,54

2,27

3,18

6,9

Calculate the sum for each pair.

1+54=55

2+27=29

3+18=21

6+9=15

The solution is the pair that gives sum 15.

a=6

b=9

Rewrite p

2

+15p+54 as (p

2

+6p)+(9p+54).

(p

2

+6p)+(9p+54)

Factor out p in the first and 9 in the second group.

p(p+6)+9(p+6)

Factor out common term p+6 by using distributive property.

(p+6)(p+9)