Factor the trinomial x3-2x2-15x Write each factor as a polynomial in descending order?

Answer 1

xxx-2xx-15x

x(xx-2x-15)

Factor (long):

axx+bx+c

a=1

b=-2

c=-15

Multiply a and c:

1*-15=-15

Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):

-15=-1*3*5

-15=3*-5, -3*5

Rewrite axx+bx+c into axx+dx+ex+c:

x(xx+3x-5x-15)

Factor sets of terms (ie axx+dx, and ex+c):

x(xx+3x-5x-15)

x(x(x+3)-5(x+3))

Combine like terms:

x(x-5)(x+3)

Factor (short):

-if trinomial is written in the form of 1xx+bx+c it can be written in the form of (x+d)(x+e) where d and e are multiples of c that add up to b

x(xx-2x-15)

Multiply a and c:

1*-15=-15

Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):

-15=-1*3*5

-15=3*-5, -3*5

x(x+3)(x-5)