Question

find the values m and n so that a polynomial p(x)=x3-mx2-13x+n has x-1 and x+3 as factors.

Answer 1

if x-1 is a factor then p(1)=0

ie 1-m-13+n=0

-m+n=12.......[1]

if x+3 is a factor then p(-3)=0

ie -27-9m+39+n=0

-9m+n=-12..........[2]

[1]-[2]  -m+n+9m-n=24

8m=24

m=3

substituting in [1]  n=15

Answer 2

m=x-1
n=17x-3
p(x)=x3-(x-1)x2-13x+(15x-3)
=x2+2x-3
=(x+3)(x-1)