Question

verify that (x-1) (x-2)and (2x+1) are the factors of polynomial 2x^3 -5x^2 +x +2

Answer 1

x-1=0
x=1
2x^3 -5x^2+x+2
2(1) ^3-5(1) ^2+1+2
2-5+1+2
0
so x-1 is a factor
x-2=0
x=2
2(2) ^3-5(2) ^2+2+2
16-20+2+2
=0
so x-2 is a factor
2x+1=0
x=-1/2
2(-1/2) ^3-5(-1/2) ^2-1/2+2
0
so 2x+1 is a factor

Answer 2

x-1 = 0
x = 1
2x^ 3 - 5x^ 2 + x + 2
2-5+1+2 = 0
x-2 = 0
x = 2
2* 8 - 5*4+2+2
16 - 20 +4 = 0
2x+1 =0
x = -1\2
2* -1\8 - 5*1\4 -1\2 + 2
- 1\4 - 5\4 +3\2 = 0
-6\4 + 3\2 =0
-3\2 + 3\2 =0
0=0

hence are proved