Question

Is x/2 + 1/3 a factor of x^3-3x^2+5x-2

Answer 1

First notice that

x=1

is a solution of

x3

+

x2

−5x+3=0

So

(x−1)

is a factor.

Let's use synthetic division to find.

x3

+

x2

−5x+3=

(x−1)

(

x2

+2x−3)

Notice that

x=1

is a root of

x2

+2x−3=0

So there's another factor

(x−1)

x3

+

x2

−5x+3=

(x−1)

(x−1)

(x+3)

5

Answer 2

no. it is not the the factor